Women in Analysis and PDE (Trends in Mathematics, 5)

Preface
Contents
Recovery of an Initial Condition from Later Time Samples
	1 Introduction
	2 Reconstruction Based on Later Time Samples
		2.1 The Heat Equation
		2.2 The Laplace Equation
		2.3 The Wave Equation with Variable Coefficients
	3 Current Research
	References
McKean-Vlasov SPDEs with Additive Noise as Limits of Weighted Interacting Particle Systems
	1 Introduction
		1.1 Statement of Main Result
	2 Heuristics
	References
Strong Birkhoff–James Orthogonality of Compact Operators on Hilbert Spaces
	1 Standard BJ Orthogonality
	2 Strong (Modular) Types of BJ Orthogonality
	3 Results
	References
Constructions of Dual Frames Compensating for Erasures with Implementation
	1 Introduction and Notation
	2 Constructions Based on the Canonical Dual
	3 Constructions Based on an Arbitrary Dual Frame
	4 Implementation and Computational Efficiency
	References
On Differential Systems in Sobolev Spaces with Generic Inhomogeneous Boundary Conditions
	1 Boundary-Value Problems
	2 Solvability
	3 Examples
	4 Continuity of Solutions in a Parameter
	5 Comments and Remarks
	References
Amenability of Semihypergroups
	1 Introduction
	2 Preliminaries
	3 Amenability of AP(K)
	4 Topological Amenability
	References
On Pseudo-Difference Operators on the Lattice Zn
	1 Introduction
	2 Calculus on Symbols
	3 Applications
		3.1 Boundedness on 2(Zn)
		3.2 Boundedness and Compactness on p(Zn)
	4 Examples
	References
Coercive inequalities on Step-Two Carnot Groups
	1 Introduction
	2 Coercive Inequalities on Step-Two Carnot Groups
	3 Coercive Inequalities in Higher Dimensional Anisotropic Heisenberg Group
	References
The Laplace Transform in Dunkl Theory
	1 Introduction
	2 Motivation: Analysis on Hermitian Matrices
	3 The Dunkl Setting and Laplace Transform in Type A
	4 Riesz Distributions in the Dunkl Setting
	5 The Cherednik Kernel and Non-symmetric Jack Polynomials
	6 Laplace Transform Identities
	7 Some Applications of the Master Theorem
	References
Asymptotic Analysis for Generalized Functions Using Frames
	1 An Introduction to Generalized Asymptotic Analysis
	2 Preliminaries
		2.1 Notations
		2.2 Spaces of Test Functions and Distributions
		2.3 Orthonormal Wavelet Basis
		2.4 Frames
	3 Asymptotic Behavior of Distributions
		3.1 Quasiasymptotic Behavior of Distributions
		3.2 S-Asymptotic Behavior of Distributions
	4 Asymptotic Results for Distributions of Exponential Type Through Gabor Frames
	5 Asymptotic Results for Tempered Distributions Through Wavelets
	6 Asymptotic Results for Tempered Distributions Through Localized Frames
	References
On Octonionic Harmonic Projection Operators
	1 Introduction
	2 The Octonionic Setting
		2.1 The Octonionic Sphere
		2.2 A Heuristic Motivation
	3 The Octonionic Bound on Diagonal Strips
	References
Generalised Fock Spaces
	1 Introduction
	2 Preliminaries
		2.1 Classical Fock Space
		2.2 Generalised Fractional Derivatives
	3 Generalised Fock Spaces
		3.1 Fractional 2-Space
		3.2 Fractional Fock Space Fφ
	References
Time-Frequency Analysis and Metaplectic Operators
	1 Introduction
	References
A Characterization of Compact Weighted SG Pseudo-Differential Operators
	1 Introduction
	2 Sobolev Spaces
	3 Compact SG M-Elliptic Pseudo-Differential Operators
	References
Global Analytic Solutions and Symmetric Waves of the 0-Equation
	References
On the Green\'s Function of the Perturbed Laplace-Beltrami Operator with a Finite Number of Punctured Points on the Two-Dimensional Sphere
	1 Introduction
	2 The Known Facts About the Laplace-Beltrami Operator
	3 Delta-Shaped Perturbations of the Laplace-Beltrami Operator
	References
Mixed Boundary Value Problem for the Helmholtz Equation in a Model 2D Double Angular Domain
	1 Introduction and Formulation of the Main Result
	2 Boundary Integral Equation of the Model Problem
	3 Investigation of the Boundary Integral Equation of the Model Problem
	References
On Hyperbolic Equations with Space-Dependent Coefficients: C∞ Well-Posedness and Levi Conditions
	1 Introduction
	2 The Case m=2
	3 Third Order Hyperbolic Equations in Higher Space Dimension
	4 Levi Conditions for Higher Order Hyperbolic Equations
	References
Covering Numbers of the Unit Ball of Reproducing Kernel Hilbert Space of Zonal Positive Definite Kernels
	1 Introduction
		1.1 Initial Concepts
		1.2 Content of the Paper
	2 Covering Numbers
	3 The Weierstrass Fractal Kernel
		3.1 Proof of Theorem 3.2
	4 The Schoenberg Kernel
	References
Recent Examples of Hypersemitoric Systems and First Steps Towards a Classification: A Brief Survey
	1 Introduction
	2 Toric, Semitoric, Hypersemitoric Systems, and Hamiltonian S1-Spaces
	3 Explicit Examples of Hypersemitoric Systems
	4 Classification of Hypersemitoric Systems?
	References
The Spaces of Ultradistributions Over Rd+ and the Weyl Calculus of Pseudo-Differential Operators
	1 Introduction
	2 Some Matters of Notation and Preliminaries
	3 The Spaces Gαβ(Rd+) and the Modified Fractional Powers of the Partial Hankel-Clifford Transform
	4 Weyl Calculus on Gelfand-Shilov Spaces with Symbols from Spaces Defined on Rd+
	References
Nonlinear Control Problems with Fractional Derivatives
	1 Introduction
	2 Systems of Fractional Differential Equations
	3 Linear Control Problems with the Caputo Fractional Derivatives
	4 Controllability of a Symmetric Quasilinear System
	References
Some Generalizations of Fixed Circle
	1 Introduction
	2 Generalizations of Fixed Circle
	3 Conclusion
	4 Open Problem
	References
Investigating Some Measurements on the Optimal Dual Frames for Erasures
	1 Introduction
	2 Results
	References
A Short Essay on the Special Functions of Fractional Calculus
	1 Basic Definitions
	2 A Few Basic Results on Multi-index M-L Functions
	3 Relations of SF of FC with the Operators of FC
	4 A Small Part of a Long List of SF of FC, for More See 25:VK-GuideSF
	References
Quantum Dissipative Systems in Infinite Dimensions
	1 Introduction
	2 The Infinite Quantum System
		2.1 Noncommutative Dirichlet Forms
	3 Examples of Models
		3.1 Quantum Hypocoercive Dissipative Semigroups
	4 Decay to Equilibrium Further Directions
	References
Operator Semigroups and Generators Associated to StochasticProcesses
	1 Introduction
	2 Markov and Levy Processes
	3 Semigroups Related to Levy Processes
	4 Generators of Semigroups, DOs, and Operators with Kernels
	References
Strong and Weak Type Estimates for the Littlewood-Paley Operator g*λ,ψ with Non-convolution Kernel
	1 Introduction
	2 The Main Result
	References
Generalized Holomorphic Functions: Sketches of a New Theory
	1 Introduction
		1.1 The Ring of Robinson Colombeau Numbers
	2 Generalized Holomorphic Functions
		2.1 Hyperlimit and Little-oh
		2.2 Complex Differentiable Function
	3 Conclusions
	References
On an Inverse Time-Dependent Control Function Problem for the Time-Fractional Diffusion Equation
	1 Introduction
	2 Preliminaries
	3 Main Result
	References
Asymptotic Behavior of Solutions to the Extension Problem for the Fractional Laplacian on Noncompact Symmetric Spaces
	1 Introduction
	2 Noncompact Riemannian Symmetric Spaces
	3 The Fractional Laplacian and the Caffarelli-Silvestre Extension
		3.1 Large Time Behavior of the Caffarelli-Silvestre Extension Kernel
	4 Proof of Theorem 1.1
	References
A Brief Excursus on Mixed Operators in Peridynamics
	1 Introduction
	2 Results
	3 Applications to Evolutionary Problems
	References
On Some Local and Nonlocal Variational Problems
	1 Introduction
	2 Regularity of Local Minimizers
	References
Virus Diffusion Modeling via Fractional Stochastic Differential Equations
	1 Introduction
	2 Ingredients
		2.1 Polynomial Chaos Expansions of Stochastic Processes
		2.2 Caputo-Fabrizio Fractional Derivatives
		2.3 Stochastic Differential Equations
	3 Modeling the Virus Diffusion via Droplets in a Closed Space
	4 Modeling the Virus Diffusion Within the Host Tissue Cells
	References
Acoustic Wave Propagation Through a Cluster of Hard Upright Cylinders: Porous Media and Radiative Transfer Approach
	1 Introduction
	2 Physical Setup and Acoustic Wave Propagation
	3 Porous Media Approach
		3.1 Radiation Transfer Approach
	4 Conclusions
	References
A Note on Hardy Inequalities in Metric Measure Spaces for the Case p=1
	1 Introduction
	2 Preliminaries
	3 Main Results and Applications
		3.1 Hardy Inequalities on Homogeneous Lie Groups
		3.2 Hardy Inequalities on Hyperbolic Spaces
	References
Coincidence Degree and Fixed Point Theory Applied to the Study of Solutions of a Nonlinear Fractional Boundary Value Problem
	1 Introduction
	2 Auxiliary Material and Methods
	3 Main Results
	4 Conclusions
	References
Degenerate Diffusion Equation with the Hadamard Time-Fractional Derivative
	1 Introduction
	2 Preliminaries
		2.1 The Dirichlet Problem
		2.2 The Neumann Problem
		2.3 The Cauchy Problem in RN
	3 Main Results
	References
On the Multipliers of Fourier Series in the Generalized Haar System
	1 Introduction
	2   np,r (Lq) Spaces and Its Properties
	3 The Main Result
	References
Hardy Inequalities on Metric Measure Spaces for Different Indices p and q
	1 Introduction
	2 The Case 1< p ≤q< ∞
	3 The Case 00
	References