Extended Abstracts 2021/2022 : Ghent Analysis and PDE Seminar / edited by Michael Ruzhansky, Karel Van Bockstal.

Format:

Book

Contributor:

Ruzhansky, M. (Michael), editor.

Van Bockstal, Karel, editor.

Series:

Research Perspectives Ghent Analysis and PDE Center, 2948-1732 ; 2

Language:

English

Subjects (All):

Mathematical analysis.

Functional analysis.

Analysis.

Functional Analysis.

Local Subjects:

Analysis.

Functional Analysis.

Physical Description:

1 online resource (302 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024.

Summary:

This book offers an overview of the research results presented by group members and guests of the Ghent Analysis & PDE Center during the weekly seminar that took place from 2021 to 2022. It is an informal event of the Analysis & PDE Center and associated researchers, where everyone can present their work or relevant literature for about 20-30 minutes. The seminar aims to exchange ideas and foster effective learning and collaboration. In this book, group members and guests summarise their results presented during the seminar and provide outlooks for future work. In this way, the book also provides an overview of the recent developments in the Ghent Analysis & PDE Center. The main topics are functional analysis, Fourier analysis, noncommutative analysis, geometric analysis, partial differential equations of different types, harmonic analysis, functional inequalities, pseudo-differential operators, fractional derivatives, special functions, microlocal analysis, inverse problems and imaging. The target audience of this book is any researcher working in the above fields. .

Contents:

Part I Analysis

A note on a Capelli operator and its resonance

Schatten-von Neumann classes Sp on the torus for 0 < p ≤ 2

Log-Sobolev and Nash inequalities on graded groups

One-sided Hardy-Littlewood maximal function on generalised Lorentz spaces

Remarks on gradient Yamabe solitons

Boundedness of Fourier multipliers on fundamental domains of lattices

Pointwise domination and weak L1 boundedness of Littlewood-Paley operators via sparse operators

Hp Lp boundedness of Fourier multipliers on graded Lie groups

On a reverse integral Hardy inequality on polarisable metric measure space

Logarithmic Sobolev inequalities of fractional order on noncommutative tori

The Prabhakar fractional q-integral and q-differential operators

A note on weak type boundedness of pseudo-differential operators on rank one symmetric spaces of noncompact type

Lp-Lq norms ofspectral multipliers

Estimates for oscillatory integrals with discontinuous amplitude

The unitary dual of the Heisenberg group over Rp

Critical Sobolev-type identities and inequalities on stratified Lie groups

Part II Partial differential equations

Anisotropic Picone type identities for general vector fields and some applications

An equivalence between the Neumann problem and its boundary domain integral equation systems for Stokes equations

Short note on generalised bivariate Mittag-Leffler-type functions

Inverse problems for time-fractional mixed equation involving the Caputo fractional derivative

Time dependent inverse source problems for integrodifferential Kelvin-Voigt system

A nonlocal initial conditional boundary value problem on metric graph

Second-order semiregular non-commutative harmonic oscillators: the spectral zeta function

Global well-posedness with loss of regularity for a class of singular hyperbolic Cauchy problems

On a mixed equationinvolving Prabhakar fractional order integral-differential operators

Inverse problem of determining a time-dependent source in a fractional Langevin-type partial differential equation

Very weak solution of the discrete wave equation for harmonic oscillator

An estimate for the multivariate Mittag-Leffler function

Part III Mathematical modelling

Mathematical modelling of the Lomb-Scargle method in astrophysics

The application of physics informed networks to solve hyperbolic partial differential equations with nonconvex flux function and diffusion term

Fractional differential equations: a primer for structural dynamics applications

Text matching as time series matching

Performing Particle Image Segmentation on an Extremely Small Dataset

Two-dimensional dispersed composites on a square torus.

Notes:

Includes bibliographical references.

ISBN:

9783031425394

3031425391