相关论文: Elements of harmonic analysis, 5

In this paper we explore homogeneous spaces Z=G/H of a a real reductive Lie group G with a closed connected subgroup H. The investigation concerns the decay at infinity of smooth functions on Z, and L^p-integrability of matrix coefficients.…

The direct and inverse spectral problems are solved for a wide subclass of the class of Schwarz matrices. A connection between the Schwarz matrices and the so-called generalized Hurwitz polynomials is found. The known results due to H. Wall…

These notes, connected to a "potpourri" topics course currently underway, are concerned with some interrelated themes of polynomials, functions on the unit circle or interval, and norms.

This paper is a companion paper to [G4], where sharp estimates are proven for Fourier transforms of compactly supported functions built out of two-dimensional real-analytic functions. The theorems of [G4] are stated in a rather general…

We consider harmonic polynomials of real variables $x,y,z$ that are eigenfunctions of the rotations about the axis $z$. They have the form $(x\pm yi)^{n}p(x,y,z)$, where $p$ is a rotation invariant polynomial. Let ${\mathfrak R}_{m}$ be the…

These are some basic notes concerning Holder and Lipschitz classes on metric spaces.

Building on the mapping relations between analytic functions and periodic functions using the abstract operators $\cos(h\partial_x)$ and $\sin(h\partial_x)$, and by defining the Zeta and related functions including the Hurwitz Zeta function…

This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…

This paper is the continuation of the study on discrete harmonic analysis related to Jacobi expansions initiated in [1]. Considering the operator $\mathcal{J}^{(\alpha,\beta)}=J^{(\alpha,\beta)}-I$, where $J^{(\alpha,\beta)}$ is the…

In this note, we highlight the impact of the paper G. H. Hardy, A theorem concerning Fourier transforms, J. Lond. Math. Soc. (1) 8 (1933), 227--231 in the community of harmonic analysis in the last 90 years, reviewing, on the one hand, the…

Let s be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fr\'echet algebra L(s',s) of the so-called smooth operators. We also characterize closed commutative *-subalgebras of L(s',s)…

We introduce and study properties of certain new harmonic function spaces on products of upper half-spaces.Norm estimates for the so-called expanded Bergman projections are obtained.Sharp theorems on multipliers acting on certain Sobolev…

We give the exact contributions of Harish-Chandra transform, $(\mathcal{H}f)(\lambda),$ of Schwartz functions $f$ to the harmonic analysis of spherical convolutions and the corresponding $L^{p}-$ Schwartz algebras on a connected semisimple…

In this paper we present generalisations of Paley-Wiener type theorems to Mellin and (Laplace-)Fourier transforms of rapidly decreasing smooth functions with positive support and log-polyhomogeneous asymptotic expansion at zero. This…

These notes, associated with a topics course, are concerned with Hausdorff measures and Lipschitz functions on metric spaces.

The purpose of this note is to discuss several results that have been obtained in the last decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than aiming at full generality, we focus on several…

We suggest the point of view that the Schubert classes of the affine Grassmannian of a simple algebraic group should be considered as Schur-positive symmetric functions. In particular, we give a geometric explanation of the Schur positivity…

We study integration in a class of Hilbert spaces of analytic functions defined on the $\mathbb{R}^s$. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss-Hermite…

These lecture notes explain the construction and basic properties of the wonderful compactification of a complex semisimple group of adjoint type. An appendix discusses the more general case of a semisimple symmetric space.

This proposal relates to the design, analysis and application of a novel numerical scheme for the solution of axisymmetric scattering problems. To this end, a procedure is introduced to iteratively evaluate the solution of the…