The Abel, Fourier and Radon transforms on symmetric spaces

In this paper we prove a new inversion theorem and a refinement of an old support theorem for two Radon transforms on a symmetric space. Included are some new identities for the Abel transform and some results about the Fourier transform from a joint work with Rawat, Sengupta and Sitaram.Comment: 24 page

Spherical Functions on Riemannian Symmetric Spaces

This paper deals with some simple results about spherical functions of type $\delta$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_\sigma$ functions.Comment: 15 page

The Paley-Wiener Theorem and the Local Huygens' Principle for Compact Symmetric Spaces

We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type of their (discrete) Fourier transforms. We also provide three independent new proofs of the strong Huygens' principle for a suitable constant shift of the wave equation on odd-dimensional spaces from our class.Comment: 26 pages, 1 figur

AKARI near-infrared background fluctuations arise from normal galaxy populations

We show that measurements of the fluctuations in the near-infrared background (NIRB) from the AKARI satellite can be explained by faint galaxy populations at low redshifts. We demonstrate this using reconstructed images from deep galaxy catalogs (HUGS/S-CANDELS) and two independent galaxy population models. In all cases, we find that the NIRB fluctuations measured by AKARI are consistent with faint galaxies and there is no need for a contribution from unknown populations. We find no evidence for a steep Rayleigh-Jeans spectrum for the underlying sources as previously reported. The apparent Rayleigh-Jeans spectrum at large angular scales is likely a consequence of galaxies being removed systematically to deeper levels in the longer wavelength channels.Comment: Submitted to MNRAS Letter

Shintani functions, real spherical manifolds, and symmetry breaking operators

For a pair of reductive groups $G \supset G'$, we prove a geometric criterion for the space $Sh(\lambda, \nu)$ of Shintani functions to be finite-dimensional in the Archimedean case. This criterion leads us to a complete classification of the symmetric pairs $(G,G')$ having finite-dimensional Shintani spaces. A geometric criterion for uniform boundedness of $dim Sh(\lambda, \nu)$ is also obtained. Furthermore, we prove that symmetry breaking operators of the restriction of smooth admissible representations yield Shintani functions of moderate growth, of which the dimension is determined for $(G, G') = (O(n+1,1), O(n,1))$.Comment: to appear in Progress in Mathematics, Birkhause

Wave and Klein-Gordon equations on hyperbolic spaces

We consider the Klein--Gordon equation associated with the Laplace--Beltrami operator $\Delta$ on real hyperbolic spaces of dimension $n\!\ge\!2$; as $\Delta$ has a spectral gap, the wave equation is a particular case of our study. After a careful kernel analysis, we obtain dispersive and Strichartz estimates for a large family of admissible couples. As an application, we prove global well--posedness results for the corresponding semilinear equation with low regularity data.Comment: 50 pages, 30 figures. arXiv admin note: text overlap with arXiv:1010.237

Can (Electric-Magnetic) Duality Be Gauged?

There exists a formulation of the Maxwell theory in terms of two vector potentials, one electric and one magnetic. The action is then manifestly invariant under electric-magnetic duality transformations, which are rotations in the two-dimensional internal space of the two potentials, and local. We ask the question: can duality be gauged? The only known and battled-tested method of accomplishing the gauging is the Noether procedure. In its decanted form, it amounts to turn on the coupling by deforming the abelian gauge group of the free theory, out of whose curvatures the action is built, into a non-abelian group which becomes the gauge group of the resulting theory. In this article, we show that the method cannot be successfully implemented for electric-magnetic duality. We thus conclude that, unless a radically new idea is introduced, electric-magnetic duality cannot be gauged. The implication of this result for supergravity is briefly discussed.Comment: Some minor typos correcte

Can the Near-IR Fluctuations Arise from Known Galaxy Populations?

Spatial Fluctuations in the Cosmic Infrared Background have now been measured out to sub-degree scales showing a strong clustering signal from unresolved sources. We attempt to explain these measurement by considering faint galaxy populations at z<6 as the underlying sources for this signal using 233 measured UV, optical and NIR luminosity functions (LF) from a variety of surveys covering a wide range of redshifts. We populate the lightcone and calculate the total emission redshifted into the near-IR bands in the observer frame and recover the observed optical and near-IR galaxy counts to a good accuracy. Using a halo model for the clustering of galaxies with an underlying LCDM density field, we find that fluctuations from known galaxy populations are unable to account for the large scale CIB clustering signal seen by HST/NICMOS, Spitzer/IRAC and AKARI/IRC and continue to diverge out to larger angular scales. Our purely empirical reconstruction shows that known galaxy populations are not responsible for the bulk of the fluctuation signal seen in the measurements and suggests an unknown population of very faint and highly clustered sources dominating the signal.Comment: 3 pages, 2 figures. To appear in proceedings of First Stars IV meeting (Kyoto, Japan; 2012