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We study the Hp-Lq boundedness of certain integral operators of fractional type.

Classical Analysis and ODEs · Mathematics 2017-03-10 Pablo Rocha

The present article deals with properties of one class of functions with complicated local structure. These functions can be modeled by certain operators of digits. Such operators were considered by the author earlier (for example, see [27,…

General Mathematics · Mathematics 2024-03-12 Symon Serbenyuk

We propose the generalization of the Fourier modal method aimed at calculating localized eigenmodes of integrated optical resonators. The method is based on constructing the analytic continuation of the structure's scattering matrix and…

Optics · Physics 2017-11-06 Dmitry A. Bykov , Leonid L. Doskolovich

In this paper various properties of global and local changes of variables as well as properties of canonical transforms are investigated on modulation and Wiener amalgam spaces. We establish several relations among localisations of…

Functional Analysis · Mathematics 2012-08-07 Michael Ruzhansky , Mitsuru Sugimoto , Joachim Toft , Naohito Tomita

Local solvability is analyzed for natural families of partial differential operators having double characteristics. In some families the set of all operators that are not locally solvable is shown to have both infinite dimension and…

Analysis of PDEs · Mathematics 2008-02-03 Michael Christ , Georgi Karadzhov , Detlef Müller

Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…

Spectral Theory · Mathematics 2024-02-09 V. A. Yurko

Examples are given of degenerate elliptic operators on smooth, compact manifolds that are not globally regular in $C^\infty$. These operators degenerate only in a rather mild fashion. Certain weak regularity results are proved, and an…

Analysis of PDEs · Mathematics 2016-09-06 Michael Christ

We introduce different notions of wave front set for the functionals in the dual of the Colombeau algebra $\Gc(\Om)$ providing a way to measure the $\G$ and the $\Ginf$- regularity in $\LL(\Gc(\Om),\wt{\C})$. For the smaller family of…

Analysis of PDEs · Mathematics 2007-05-23 Claudia Garetto

These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.

Classical Analysis and ODEs · Mathematics 2007-05-23 Stephen Semmes

The Fourier-Stieltjes and Fourier algebras B(G), A(G) for a general locally compact group G, first studied by P. Eymard, have played an important role in harmonic analysis and in the study of operator algebras generated by G. Recently,…

Operator Algebras · Mathematics 2007-05-23 Alan L. T. Paterson

This article presents a convenient approach to Fourier analysis for the investigation of functions and distributions defined in $\mathbb{T}^m \times \mathbb{R}^n$. Our approach involves the utilization of a mixed Fourier transform,…

Analysis of PDEs · Mathematics 2025-02-19 André Pedroso Kowacs

Given two real numbers, the $L^2$ functions whose Fourier transforms vanish with a certain rapidity near the given numbers are characterised as those that are expressible as the sum of a certain number of generalised finite differences that…

Classical Analysis and ODEs · Mathematics 2016-05-24 Rodney Nillsen

This paper is devoted to studying the boundedness of multilinear operartors and their commutators on generalized weighted Morrey spaces, which includes multilinear fractional maximal operator and multilinear fractional integral operator.…

Classical Analysis and ODEs · Mathematics 2023-06-27 Xi Cen , Qianjun He , Xiang Li , Dunyan Yan

In this article we study some Kramers-Fokker-Planck operators with a polynomial potential $V(q)$ of degree greater than two having quadratic limiting behavior. This work provides an accurate global subelliptic estimate for KFP operators…

Analysis of PDEs · Mathematics 2019-05-29 Mona Ben Said

In this paper we obtain degree of approximation of functions in Lp by operators associated with their Fourier series using integral modulus of continuity. These results generalize many know results and are proved under less stringent…

Classical Analysis and ODEs · Mathematics 2012-05-29 R. N. Mohapatra , B. Szal

In 1968, Israel Gohberg and Naum Krupnik discovered that local spectra of singular integral operators with piecewise continuous coefficients on Lebesgue spaces $L^p(\Gamma)$ over Lyapunov curves have the shape of circular arcs. About 25…

Functional Analysis · Mathematics 2008-10-20 Alexei Yu. Karlovich

The study of nonlocal operators of fractional type possesses a long tradition, motivated both by mathematical curiosity and by real world applications...

Analysis of PDEs · Mathematics 2022-10-04 Alessandro Carbotti , Serena Dipierro , Enrico Valdinoci

We consider a large class of physical fields $u$ written as double inverse Fourier transforms of some functions $F$ of two complex variables. Such integrals occur very often in practice, especially in diffraction theory. Our aim is to…

Analysis of PDEs · Mathematics 2022-10-18 Raphaël C. Assier , Andrey V. Shanin , Andrey I. Korolkov

The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.

Functional Analysis · Mathematics 2018-12-18 S. V. Ludkovsky

In this paper, we study the local spectral properties for both unilateral and bilateral weighted shift operators.

Functional Analysis · Mathematics 2007-05-23 A. Bourhim