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Moment functions play a basic role in probability theory. A natural generalization can be defined on hypergroups which leads to the concept of generalized moment function sequences. In a former paper we studied some function classes on hypergroup joins which play a basic role in spectral synthesis. Moment functions are also important basic blocks of spectral synthesis. All these functions can be characterized by well-known functional equations. In this paper we describe generalized moment function sequences on hypergroup joins.

Let $X=U/K$ be a compact Hermitian symmetric space, and let $\sE$ be a $U$-homogeneous Hermitian vector bundle on $X$. In a previous paper, we showed that the space of nearly holomorphic sections is well-adapted for harmonic analysis in $L^2(X,\sE)$ provided that non-trivial nearly holomorphic sections do exist. Here we investigate the problem of extending local nearly holomorphic sections to global ones and prove the existence of non-trivial nearly holomorphic sections. This extends the results on the $U$-type decomposition of $L^2(X,\sE)$ from our previous paper., 20 pages

In this paper, we consider a Brück-type result for a homogeneous differential polynomial generated by a meromorphic function.

In this paper, we present a new differential operator of arbitrary order defined by means of a Caputo-type modification of the generalized fractional derivative recently proposed by Katugampola. The generalized fractional derivative, when convenient limits are considered, recovers the Riemann–Liouville and the Hadamard derivatives of arbitrary order. Our differential operator recovers as limiting cases the arbitrary order derivatives proposed by Caputo and by Caputo–Hadamard. Some properties are presented as well as the relation between this differential operator of arbitrary order and the Katugampola generalized fractional operator. As an application we prove the fundamental theorem of fractional calculus associated with our operator.

In the present paper, it is shown that if a prime ring R admits a generalized derivation f associated with a nonzero derivation d such that either f([x^{m},y^{n}])+[x^{m},y^{n}]\in Z(R)\quad\text{for all }x,y\in R or f([x^{m},y^{n}])-[x^{m},y^{n}]\in Z(R)\quad\text{for all }x,y\in R, then R is commutative. We apply this purely ring theoretic result to obtain commutativity of Banach algebras and prove that if A is a prime Banach algebra which admits a continuous linear generalized derivation f associated with a nonzero continuous linear derivation d such that either {f([x^{m},y^{n}])-[x^{m},y^{n}]\in Z(A)} or {f([x^{m},y^{n}])+[x^{m},y^{n}]\in Z(A)} for an integer {m=m(x,y)>1} and sufficiently many {x,y} in A, then A is commutative. A similar result is obtained for a unital prime Banach algebra A which admits a nonzero continuous linear generalized derivation f associated with a continuous linear derivation d such that {d(Z(A))\neq 0} satisfying either {f((xy)^{m})-x^{m}y^{m}\in Z(A)} or {f((xy)^{m})-y^{m}x^{m}\in Z(A)} for each {x\in G_{1}} and {y\in G_{2}} , where {G_{1},G_{2}} are open sets in A and {m=m(x,y)>1} is an integer: then A is commutative.

In this article, we correct the proof of the main theorem of Gordji’s paper [M. Eshaghi Gordji, n-Jordan homomorphisms, Bull. Aust. Math. Soc. 80 2009, 1, 159–164] by a different method and generalize Zelazko’s theorem to 4-Jordan homomorphisms by considering an extra condition.

In this paper, we study varieties and characterize convolution operators on the algebras related to the new structures of KPC-hypergroups, which are a generalization of the classical ones.

In this paper, by employing a critical point theorem, we establish the existence of infinitely many solutions for fourth-order impulsive differential equations depending on two real parameters.

Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in {\widehat{G}} , the unitary dual of G, sends smooth vectors of the representation space of π to {{\mathcal{U}(\mathfrak{g})}^{*}} , the dual vector space of {\mathcal{U}(\mathfrak{g})} . The convex hull of the image of the generalized moment map for π is called its generalized moment set, denoted by {J(\pi)} . We say that {\widehat{G}} is generalized moment separable when the generalized moment sets differ for any pair of distinct irreducible unitary representations. Our main result in this paper provides a second proof of the generalized moment separability theorem for G.

The object of the present paper is to study generalized Sasakian-space-forms satisfying the curvature condition{P(\xi,Y)\cdot W=0}. Moreover, ϕ-M-projectively semisymmetric and ϕ-pseudo-projectively semisymmetric generalized Sasakian-space-forms are also studied.

In this paper, it is shown that, if R is a ∗-ring containing a nontrivial self adjoint idempotent which admits a ∗-Lie higher derivable mapping L={Ln}n∈N, then there exists an element ZX,Y (depending on X and Y) in the center Z(R) such that Ln(X+Y)=Ln(X)+Ln(Y)+ZX,Y.

In this paper, using sub-supersolution argument, we prove some existence results on positive solution for a class of nonlocal elliptic systems with multiple parameters in bounded domains.

In this paper we shall find some sufficient conditions for a uniqueness polynomial to be a strong uniqueness polynomial, as this type of problem was never investigated by researchers earlier. We also exhibit some examples to substantiate our theorems.

The main goal of this paper is to give potential theoretical approach to study the Dunkl Laplacian $\Delta_k$ which is a standard example of differential-difference operators. By introducing the Green kernel relative to $\Delta_k$, we prove that the Dunkl Laplacian generates a balayage space and we investigate the associated family of harmonic measures. Therefore, by mean of harmonic kernels, we give a characterization of all $\Delta_k$-harmonic functions on large class of open subsets $U$ of $\mathbb{R}^d$. We also establish existence and uniqueness result of a solution of the corresponding Dirichlet problem., Comment: 21 pages

In this paper, we give necessary and sufficient conditions for a homogeneous cone Ω to be symmetric in two ways. One is by using the multiplier matrix of Ω, and the other is in terms of the basic relative invariants of Ω. In the latter approach, we need to show that the real parts of certain meromorphic rational functions obtained by the basic relative invariants are always positive on the tube domains over Ω. This is a generalization of a result of Ishi and Nomura [Math. Z. 259 (2008), 604–674].

In this paper, we consider the generalized spherical functions

In this paper, we study some properties of transversal hypersurfaces of a nearly trans-Sasakian manifold. Furthermore, we give some characterizations of totally geodesic regarding such manifolds. We also prove that if

In the present paper we characterize, in terms of characters, additive functions and matrix elements of irreducible two-dimensional representations, the continuous solutions of some trigonometric functional equations for mappings defined on an arbitrary group and taking their values in a complex Hilbert space with the Hadamard product. In addition, we investigate a superstability result for these equations.

In this paper, a general theorem concerning the phi-vertical bar C,alpha vertical bar(k) summability factors of infinite series, has been proved.

In this paper, we derive new integral inequalities for functions with h -convex and h-concave first derivatives. As a consequence, we give new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are h-convex and h -concave and we point out the results for some special classes of functions. © 2014 by Walter de Gruyter Berlin/Boston 2014.

The reconstruction property for Banach spaces was introduced by Casazza and Christensen. In this paper we give a type of the reconstruction property in Banach spaces which is generated by the Toeplitz matrices and we call it the Toeplitz reconstruction property. It is proved that the standard reconstruction property in a Banach space can generate the Toeplitz reconstruction property from a given Toeplitz matrix but not conversely. Suficient conditions on infinite matrices to have the reconstruction property for a discrete signal space are given. Refereed/Peer-reviewed