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We~prove uniqueness of the Moebius invariant semi-inner product on hyperbolic-harmonic functions on the unit ball of the real n-space, i.e. on functions annihilated by the hyperbolic Laplacian on the ball., Comment: 11 pages, no figures

We~describe a Dirichlet-type space of $H$-harmonic functions, i.e. functions annihilated by the hyperbolic Laplacian on~the unit ball of the real $n$-space, as~the analytic continuation (in~the spirit of Rossi and Vergne) of the corresponding weighted Bergman spaces. Characterizations in terms of derivatives are given, and the associated semi-inner product is shown to be Moebius invariant. We~also give a formula for the corresponding reproducing kernel. Our~results solve an open problem addressed by M.~Stoll in his book ``Harmonic and subharmonic function theory on the hyperbolic ball'' (Cambridge University Press, 2016)., Comment: 25 pages, no figures

We~describe the Dirichlet space of $M$-harmonic functions, i.e.~functions annihilated by the invariant Laplacian on~the unit ball of the complex $n$-space, as~the limit of the analytic continuation (in~the spirit of Rossi and Vergne) of the corresponding weighted Bergman spaces. Characterizations in terms of tangential derivatives are given, and the associated inner product is shown to be Moebius invariant. The pluriharmonic and harmonic cases are also briefly treated., Comment: 26 pages, no figures

We~identify the standard weighted Bergman kernels of spaces of nearly holomorphic functions, in~the sense of Shimura, on~bounded symmetric domains. This also yields a description of the analogous kernels for spaces of ``invariantly-polyanalytic'' functions -- a~generalization of the ordinary polyanalytic functions on the ball which seems to be the most appropriate one from the point of view of holomorphic invariance. In~both cases, the~kernels turn out to be given by certain spherical functions, or equivalently Heckman-Opdam hypergeometric functions, and a conjecture relating some of these to a Faraut-Koranyi hypergeometric function is formulated based on the study of low rank situations. Finally, analogous results are established also for compact Hermitian symmetric spaces, where explicit formulas in terms of multivariable Jacobi polynomials are~given., Comment: 38 pages, no figures

Using the machinery of unitary spherical harmonics due to Koornwinder, Folland and other authors, we~obtain expansions for the Szeg\"o and the weighted Bergman kernels of $M$-harmonic functions, i.e.~functions annihilated by the invariant Laplacian on the unit ball of the complex $n$-space. This yields, among others, an explicit formula for the $M$-harmonic Szeg\"o kernel in terms of multivariable as well as single-variable hypergeometric functions, and also shows that most likely there is no explicit (``closed'') formula for the corresponding weighted Bergman kernels., Comment: 39 pages, no figures

We show that there is no radial balanced metric on the unit ball of the Kepler manifold with not too wild boundary behavior. Additionally, we identify explicitly the weights corresponding to radial metrics with such boundary behavior which satisfy the balanced condition as far as germs at the boundary are concerned. Related results for Poincare metrics are also established.

We study the complex geometry of generalized Kepler manifolds, defined in Jordan theoretic terms, introduce Hilbert spaces of holomorphic functions defined by radial measures, and find the complete asymptotic expansion of the corresponding reproducing kernels for K\"ahler potentials, both in the flat and bounded setting., Comment: 32 pages, no figures

In~this paper, we construct noncommutative coherent states using various families of unitary irreducible representations (UIRs) of $\g$, a connected, simply connected nilpotent Lie group, that was identified as the kinematical symmetry group of noncommutative quantum mechanics for a system of 2-degrees of freedom in an earlier paper. Likewise described are the degenerate noncommutative coherent states arising from the degenerate UIRs of $\g$. We~then compute the reproducing kernels associated with both these families of coherent states and study Berezin-Toeplitz quantization of the observables on the underlying 4-dimensional phase space, analyzing in particular the semi-classical asymptotics for both these cases., Comment: 22 pages, no figure

We give criteria for the membership of Hankel operators on the Hardy space on the disc in the Dixmier class, and establish estimates for their Dixmier trace. In contrast to the situation in the Bergman space setting, it turns out that there exist Dixmier-class Hankel operators which are not measurable (i.e. their Dixmier trace depends on the choice of the underlying Banach limit), as well as Dixmier-class Hankel operators which do not belong to the $(1,\infty)$ Schatten-Lorentz ideal. A related question concerning logarithmic interpolation of Besov spaces is also discussed., Comment: 21 pages, no figures

For a class of $O(n+1,R)$ invariant measures on the Kepler manifold possessing finite moments of all orders, we describe the reproducing kernels of the associated Bergman spaces, discuss the corresponding asymptotic expansions of Tian-Yau-Zelditch, and study the relevant Hankel operators with conjugate holomorphic symbols. Related reproducing kernels on the minimal ball are also discussed. Finally, we observe that the Kepler manifold either does not admit balanced metrics, or such metrics are not unique., Comment: 20 pages; submitted to J. Funct. Anal. on January 16, 2015

For~weights $\rho$ which are either radial on the unit ball or depend only on the vertical coordinate on the upper half-space, we describe the asymptotic behaviour of the corresponding weighted harmonic Bergman kernels with respect to $\rho^\alpha$ as $\alpha\to+\infty$. This can be compared to the analogous situation for the holomorphic case, which is of importance in the Berezin quantization as well as in complex geometry., Comment: 15 pages; submitted to J. Funct. Anal. on February 19, 2015

We give a complete description of the boundary behaviour of the Poisson kernel and the harmonic Bergman kernel of a bounded domain with smooth boundary, which in some sense is an analogue of the similar description for the usual Bergman kernel on a strictly pseudoconvex domain due to Fefferman. Our main tool is the Boutet de Monvel calculus of pseudodifferential boundary operators, and in fact we describe the boundary singularity of a general potential, trace or singular Green operator from that calculus., Comment: submitted to J. Math. Anal. Appl. on December 30 2011

Continuing our earlier investigation of the Hermite case [J. Math. Phys. 55 (2014), 042102], we study an unorthodox variant of the Berezin-Toeplitz quantization scheme associated with Laguerre polynomials. In particular, we describe a "Laguerre analogue" of the classical Fock (Segal-Bargmann) space and the relevant semi-classical asymptotics of its Toeplitz operators; the former actually turns out to coincide with the Hilbert space appearing in the construction of the well-known Barut-Girardello coherent states. Further extension to the case of Legendre polynomials is likewise discussed., Comment: 25 pages, no figures

We give examples of spectral triples, in the sense of A. Connes, constructed using the algebra of Toeplitz operators on smoothly bounded strictly pseudoconvex domains in $C^n$, or the star product for the Berezin-Toeplitz quantization. Our main tool is the theory of generalized Toeplitz operators on the boundary of such domains, due to Boutet de Monvel and Guillemin., Comment: 31 pages

We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated semi-classical asymptotics., Comment: 16 pages, no figures

We prove the Arveson-Douglas essential normality conjecture for graded Hilbert submodules that consist of functions vanishing on a given homogeneous subvariety of the ball, smooth away from the origin. Our main tool is the theory of generalized Toeplitz operators of Boutet de Monvel and Guillemin., Comment: 22 pages, no figures

We give criteria for products of Toeplitz and Hankel operators on the Fock (Segal-Bargmann) space to belong to the Dixmier class, and compute their Dixmier trace. At the same time, analogous results for the Weyl pseudodifferential operators are also obtained., Comment: 23 pages, no figures

We give criteria for boundedness of the associated Bergman-type projections on Lp-spaces on Cn with respect to generalized Gaussian weights exp(-|z|^2m). Complete characterization is obtained for 0

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them.

For a real symmetric domain $G_{\mathbb R}/K_{\mathbb R}$, with complexification $G_{\mathbb C}/K_{\mathbb C}$, we introduce the concept of "star-restriction" (a real analogue of the "star-products" for quantization of K\"ahler manifolds) and give a geometric construction of the $G_{\mathbb R}$-invariant differential operators yielding its asymptotic expansion.

We compute the Szeg\"o kernels of the unit circle bundles of homogeneous negative line bundles over a compact Hermitian symmetric space. We prove that their logarithmic terms vanish in all cases and, further, that the circle bundles are not diffeomorphic to the unit sphere in $\CC^n$ for Grassmannian manifolds of higher ranks. In particular they provide an infinite family of smoothly bounded strictly pseudo-convex domains on complex manifolds for which the log terms in the Fefferman expansion of the Szeg\"o kernel vanish and which are not diffeomorphic to the sphere. The analogous results for the Bergman kernel are also obtained., Comment: Math. Zeit, to appear

We compute the Dixmier trace of pseudo-Toeplitz operators on the Fock space. As an application we find a formula for the Dixmier trace of the product of commutators of Toeplitz operators on the Hardy and weighted Bergman spaces on the unit ball of \mathbb C^d. This generalizes an earlier work of Helton-Howe for the usual trace of the anti-symmetrization of Toeplitz operators., Comment: Proc. Amer. Math. Soc. to appear

We generalize some earlier results on a Berezin-Toeplitz type of quantization on Hilbert spaces built over certain matrix domains. In the present, wider setting, the theory could be applied to systems possessing several kinematic and internal degrees of freedom. Our analysis leads to an identification of those observables, in this general context, which admit a semi-classical limit and those for which no such limit exists. It turns out that the latter class of observables involve the internal degrees of freedom in an intrinsic way. Mathematically, the theory, being a generalization of the standard Berezin-Toeplitz quantization, points the way to applying such a quantization technique to possibly non-commutative spaces, to the extent that points in phase space are now replaced by $N\times N$ matrices., Comment: 15 pages, no pictures

For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the reproducing kernels of Sobolev spaces of holomorphic functions of any real order. This generalizes the classical result of Fefferman for the unweighted Bergman kernel. Finally, we also exhibit a holomorphic continuation of the kernels with respect to the Sobolev parameter to the entire complex plane. Our main tool are the generalized Toeplitz operators of Boutet de Monvel and Guillemin., Comment: 35 pages, no figures

We explore the possibility of extending the well-known Berezin-Toeplitz quantization to reproducing kernel spaces of vector-valued functions. In physical terms, this can be interpreted as accommodating the internal degrees of freedom of the quantized system. We analyze in particular the vector-valued analogues of the classical Segal-Bargmann space on the domain of all complex matrices and of all normal matrices, respectively, showing that for the former a semi-classical limit, in the traditional sense, does not exist, while for the latter only a certain subset of the quantized observables have a classical limit: in other words, in the semiclassical limit the internal degrees of freedom disappear, as they should. We expect that a similar situation prevails in much more general setups., Comment: 28 pages, no figures

In this review we attempt to present an overview of some of the better known quantization techniques found in the current literature and used both by physicists and mathematicians. The treatment is more descriptive than rigorous, for we aim to reach both physicists and mathematicians, including non-specialists in the field. It is our hope that an overview such as this will put into perspective the relative successes as well as shortcomings of the various techniques that have been developed and, besides delineating their usefulness in understanding the nature of the quantum regime, will also demonstrate the mathematical richness of the attendant structures., Comment: 72 pages, review article

As a substantial generalization of the technique for constructing canonical and the related nonlinear and q-deformed coherent states, we present here a method for constructing vector coherent states in the same spirit. These vector coherent states may have a finite or an infinite number of components. As examples we first apply the technique to construct vector coherent states using the Plancherel isometry for groups and vector coherent states associated to Clifford algebras, in particular quaternions. As physical examples, we discuss vector coherent states for a quantum optical model and finally apply the general technique to build vector coherent states over certain matrix domains., Comment: 30 pages

Research has shown that observers' vicarious emotional reactions to an in-group member's facial display of pleasure and pain are highly differentiated and empathetic, while responses to the expressive displays of an out-group member are relatively undifferentiated and indifferent. This study examines the effects of perceived group membership on vicarious emotional responses under conditions of symmetric (concordant) or asymmetric (discordant) contingencies between a coactor's expressive displays. Subjects (N=80) were male undergraduates paid for their participation in a study which they were told examined decision making. Subjects were told that a computer evaluated the scores of participants and made group assignments. Subjects performed decision-making tasks, with one-half of the subjects informed of a third participant (the coactor) involved. Subjects worked through a series of decisions for which they were rewarded with candy or punished by electrical shock. The coactor on videotape displayed pleasure or pain. During exposure to affectively relevant consequences (acquisition) empathetic and counter-empathetic responses were wholly determined by the contingencies operating in the situation, and appeared little affected by social categorization. The influence of group membership of a coactor acted to facilitate generalization of acquired empathy responses in response to members of an in-group following a cooperatively structured situation. (ABL)

In the management field, researchers have proposed that our future lies in building sustainable enterprises that connect industry, society, and environment (Senge and Carstedt, 2001). The firm's ultimate goal should not be just profitability (creating economic value for its shareholders); rather, it should be three-fold (creating economic, social, and environmental value) (Elkington, 1997). This goal is often referred to as triple bottom line performance. We examine the relationship between strategic sustainability practices in the apparel-textile complex and performance outcomes focusing on triple bottom line performance outcomes stemming from economic (sales increase, cost reduction, waste reduction, cycle reduction), social (social responsibility, ethics), and environmental (legal compliance, standards, codes, reduced impact) goals. From the firm perspective, we will use case studies and longitudinal research in order to contribute to both short term viability and long term competitiveness of firms in the textile industry. On the consumer side, we will focus on consumers' understanding of, attitudes toward, and interest in sustainably produced textile and apparel products. We are interested in determining the extent to which consumers will pay higher prices for textile and apparel products produced by firms that emphasize sustainability. We plan to disseminate this information to sample firms through industry briefs as a reward for their participation in our research and to the broader textile and apparel industry through our Industry Advisory Council and industry trade publications. [ABSTRACT FROM AUTHOR]

Management researchers have proposed that our future lies in building sustainable enterprises that connect industry, society and environment (Senge and Carstedt, 2001). The firm's ultimate goal should not be just profitability (creating economic value for its shareholders). Instead, its goals should be three-fold: creating economic, social, and environmental value (Elkington, 1997). This perspective is often referred to as triple bottom line performance. In this project our objective is to examine the relationship between strategic sustainability practices in the apparel-textile complex and performance outcomes focusing on triple bottom line performance outcomes stemming from economic (sales increase, cost reduction, waste reduction, cycle reduction), social (social responsibility, ethics) and environmental (legal compliance, standards, codes, reduced impact) goals. We are examining these issues from the dual perspectives of firms and consumers. First, we will focus on firms in three areas of the textile industry: apparel, hospitality, and artificial turf. The second facet of the work will focus on consumers of textile and apparel products and examine their understanding, attitudes toward and interest in sustainably-produced textile and apparel products. We are interested in determining the extent to which consumers will pay a premium for textile and apparel products that firms emphasizing sustainability produce. More importantly, we will learn more about consumption patterns for sustainable textile and apparel products. We plan to disseminate this information to firms that agree to participate in our research via industry briefs and to the broader textile and apparel industry through an IndustryAdvisory Council we are forming as well as through industry trade publications. [ABSTRACT FROM AUTHOR]

Given the global nature of competition and the emphasis on cost, U.S. textile producers typically are unable to compete with offshore manufacturers strictly on a price basis. The failure of many textile and apparel companies to differentiate themselves has had a negative effect on their profitability and viability throughout the value chain. The ability to store, capture and disseminate knowledge within and across organizational boundaries as a source of competitive advantage has been a key challenge for managers. As product lifecycles have decreased and environmental complexity and volatility have increased, the textile industry's need to manage knowledge has intensified. This project examined the process of acquisition, retention, maintenance, and retrieval of knowledge both within the firm and across the value chain. First, we developed case studies to examine how firms manage knowledge internally and externally through relationships with downstream partners in their value-chains. To assess the "state of the industry" regarding knowledge management systems we focused on two companies, DuPont Textiles and Interiors (Invista) and CINTAS. Based on the information gathered from interviews with company personnel and our review of the literature, we developed a survey instrument to measure internal and external knowledge activities across the value chain. The survey was launched on the fall of 2005 and multiple waves of data have been collected. The results of our analysis show that there are gaps in how both internal and external knowledge is managed within the industry. [ABSTRACT FROM AUTHOR]