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In this article, we prove that a complex cone is a set of injectivity for the twisted spherical means for the class of all continuous functions on $\mathbb C^n$ as long as it does not completely lay on the level surface of any bi-graded homogeneous harmonic polynomial on $\mathbb C^n.$ Further, we produce examples of such level surfaces., Comment: This article is accepted in Trans. Amer. Math. Soc. arXiv admin note: text overlap with arXiv:1204.2773

In this article, we review the Weyl correspondence of bigraded spherical harmonics and use it to extend the Hecke-Bochner identities for the spectral projections $f\times\varphi_k^{n-1}$ for function $f\in L^p(\mathbb C^n)$ with $1\leq p\leq\infty.$ We prove that spheres are sets of injectivity for the twisted spherical means with real analytic weight. Then, we derive a real analytic expansion for the spectral projections $f\times\varphi_k^{n-1}$ for function $f\in L^2(\mathbb C^n).$, Comment: 18 pages, appeared in Israel J. Math

In this article, we prove that any pair of perpendicular planes is a set of injectivity for the twisted spherical means (TSM) for $L^p(\mathbb C^n) (n\geq2)$ with $1\leq p\leq2.$ Then, we imitate that any Coxeter system of even number of planes is a set of injectivity for the TSM for $L^p(\mathbb C^n).$ We further observe that a set $S_R^{2n-1}\times\mathbb C$ is a set of injectivity for the TSM for a ceratin class of functions on $\mathbb C^{n+1}.$, Comment: This article is accepted in J. Funct. Anal. jointly with arXiv:1103.4571

It is well known that a line in $\mathbb R^2$ is not a set of injectivity for the spherical means for odd functions about that line. We prove that any line passing through the origin is a set of injectivity for the twisted spherical means (TSM) for functions $f\in L^2(\mathbb C),$ whose each of spectral projection $ e^{\frac{1}{4}|z|^2}f\times\varphi_k$ is a polynomial. Then, we prove that any Coxeter system of even number of lines is a set of injectivity for the TSM for $L^q(\mathbb C),~1\leq q\leq2.$, Comment: This article is accepted in J. Funct. Anal. jointly with arXiv:1204.2773

In this article, we show that the spheres $S_R(o)=\{z\in\mathbb C^n: |z|=R\}$ are sets of injectivity for the weighted twisted spherical means (WTSM) for a suitable class of functions on $\mathbb C^n$. The weights here are spherical harmonics on $S^{2n-1}.$ In general, the question of set of injectivity for the twisted spherical means (TSM) with real analytic weight is still open. We would like to refer to \cite{NRR}, for some results on the sets of injectivity for the spherical means with real analytic weights in the Euclidean setup., Comment: Published: J. Fourier Anal. Appl., 18(2012), no. 3, 592-608. arXiv admin note: text overlap with arXiv:1103.4571

Let $Z_{r,R}$ be the class of all continuous functions $f$ on the annulus $\Ann(r,R)$ in the real hyperbolic space $\mathbb B^n$ with spherical means $M_sf(x)=0$, whenever $s>0$ and $x\in \mathbb B^n$ are such that the sphere $S_s(x)\subset \Ann(r, R) $ and $B_r(o)\subseteq B_s(x).$ In this article, we give a characterization for functions in $Z_{r,R}$. In the case $R=\infty$, this result gives a new proof of Helgason's support theorem for spherical means in the real hyperbolic spaces., Comment: published: Proc. Indian. Acad. Sci., 121 (2011), No.3, 311-325

Let $Z(Ann(r,R))$ be the class of all continuous functions $f$ on the annulus $Ann(r,R)$ in $\mathbb C^n$ with twisted spherical mean $f \times \mu_s(z)=0,$ whenever $z\in \mathbb C^n$ and $s >0$ satisfy the condition that the sphere $S_s(z)\subseteq Ann(r, R) $ and ball $B_r(0)\subseteq B_s(z).$ In this paper, we give a characterization for functions in $Z(Ann(r,R))$ in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in $\mathbb C^n$ which improve some of the earlier results., Comment: Published: Annales de l'institut Fourier, 59 no. 6 (2009), p. 2509-2523

Since the early 1960s, Abrikosov-Gorkov theory has been used to describe superconductors with paramagnetic impurities. Interestingly, the density of states resulting from the theoretical framework has to date only been known approximately, as a numeric solution of a complex polynomial. Here we introduce an exact analytic solution for the density of states of a superconductor with paramagnetic impurities. The solution is valid in the whole regime of Abrikosov-Gorkov theory; both where there is an energy gap and gapless. While of fundamental interest, we argue that this solution also has computational benefits in the evaluation of integrals for tunneling conductances and allows for an analytic description of materials with densities of states that are modeled from the basic Abrikosov-Gorkov density of states., Comment: 5 pages, 1 figure

Thin films of the molecular magnet Mn12-acetate, [Mn12 O12(CH3COO)16 (H2O)4] 2CH3COOH 4H2O, have been prepared using a laser ablation technique with a nitrogen laser at low laser energies of 0.8 and 2 mJ. Chemical and magnetic characterizations show that the Mn12-acetate cores remain intact and the films show similar magnetic properties to those of the parent molecular starting material. In addition, the magnetic data exhibit a peak in the magnetization at 27 K indicating the creation of an additional magnetic phase not noted in previous studies of crystalline phases., Comment: 8 pages, 5 figures, In Press - J. Mag. Mag. Mat

We report the observation of large ($\sim 40%$) laser-induced above-bandgap transparency in GaAs at room temperature. The induced transparency is present only during the pulse width of the driving midinfrard laser pulses and its spectral shape is consistent with a laser-induced blue shift of the band edge. Our simulations based on the dynamic Franz-Keldysh effect reproduce the salient features of the experimental results, demonstrating in particular that the amount of the band edge shift is approximately given by the ponderomtive potential., Comment: 4 pages, 4 figures

We present evidence for the coexistence of ferromagnetic metallic and charge ordered insulating phases in strained thin films of La$_{0.67}$Ca$_{0.33}$MnO$_3$ at low temperatures. Such a phase separated state is confirmed using low temperature magnetic force microscopy and magnetotransport measurements. This phase separated state is not observed in the bulk form of this compound and is caused by the structural inhomogeneities due to the non-uniform distribution of strain in the film. The strain weakens the low temperature ferromagnetic metallic state and a charge ordered insulator is formed at the high strain regions. The slow dynamics of the transport properties of the mixed phase is illustrated by measurements of the long time scale relaxation of the electrical resistance., Comment: 7 pages ReVTeX, 7 figures included, submitted to Phys. Rev. B