Recent Advances in Mathematical Analysis : Celebrating the 70th Anniversary of Francesco Altomare / edited by Anna Maria Candela, Mirella Cappelletti Montano, Elisabetta Mangino.

Format:

Book

Contributor:

Candela, Anna Maria, editor.

Cappelletti Montano, Mirella, editor.

Mangino, Elisabetta, editor.

Series:

Trends in Mathematics, 2297-024X

Language:

English

Subjects (All):

Functional analysis.

Approximation theory.

Functional Analysis.

Approximations and Expansions.

Local Subjects:

Functional Analysis.

Approximations and Expansions.

Physical Description:

1 online resource (XVIII, 463 p. 4 illus. in color.)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2023.

Summary:

This book collects selected peer reviewed papers on the topics of Nonlinear Analysis, Functional Analysis, (Korovkin-Type) Approximation Theory, and Partial Differential Equations. The aim of the volume is, in fact, to promote the connection among those different fields in Mathematical Analysis. The book celebrates Francesco Altomare, on the occasion of his 70th anniversary.

Contents:

Intro

Rector's Foreword

Preface

From ReDiMA 2021 Opening Ceremony

Contents

List of Contributors

On Wachnicki's Generalization of the Gauss-Weierstrass Integral

1 Introduction

2 The Operators

3 The Asymptotic Expansion

4 Localization Result

References

Generalized Subharmonic and Weakly Convex Functions

2 A Conjecture

3 A Result Related to the Conjecture

A Strong Variant of Weyl's Theorem Under Functional Calculus and Perturbations

2 Definitions and Preliminary Results

3 S-Weyl's Theorem

4 S-Weyl's Theorem Under Commuting Perturbations

Multiplication and Convolution Topological Algebras in Spaces of ω-Ultradifferentiable Functions of Beurling Type

3 The Algebras (OM,ω(RN),·), (Sω(RN),·), (Sω(RN),) and (OC,ω(RN),)

4 Hypocontinuity and Discontinuity

4.1 Hypocontinuity

4.2 Discontinuity

Higher Order Elliptic Equations in Generalized Morrey Spaces

3 Statement of the Problem and the Main Result

Norm and Essential Norm of Composition Operators Mapping into Weighted Banach Spaces of Harmonic Mappings

2 Boundedness, Compactness, and Operator Norm

3 Essential Norm

4 Applications to Hilbert Spaces of Harmonic Mappings

4.1 The Harmonic Hardy Space

4.2 The Harmonic Bergman Space

4.3 The Harmonic Dirichlet Space

5 An Application to the Harmonic Bloch Space

Generalized Gaussian Estimates for Elliptic Operators with Unbounded Coefficients on Domains

2 Preliminaries

2.1 Sesquilinear Forms and Properties of the Associated Semigroups

2.2 Finite-Dimensional Sesquilinear Forms with Real Coefficients.

3 A Second Order Elliptic Operator on Ω with Unbounded Coefficients

4 Gaussian Estimates

5 The Lp-Analyticity of the Semigroup (T(t))

6 Examples

An Existence Result for Perturbed (p,q)-Quasilinear EllipticProblems

2 Preliminary Material

2.1 Quasi-Eigenvalues for the Operator -p-q

2.2 Variational Tools

2.3 Essential Values

3 The Unperturbed Case

4 The Perturbed Case

Weighted Composition Operators on Weighted Spaces of Banach Valued Analytic Functions

2 The Operator Wψ,φ on Weighted Banach Spaces of Vector-Valued Functions

3 Inductive Limits of Weighted Banach Spaces of Vector-Valued Functions

4 Projective Limits of Weighted Banach Spaces of Vector-Valued Functions

Existence of Positive Solutions of Nonlinear Second Order Dirichlet Problems Perturbed by Integral Boundary Conditions

2 Linear Part: Green's Function

2.1 Case γ=0

2.2 Case γ&gt

0

2.3 Case γ&lt

3 Nonlinear Problem

3.1 Problem (2), (3)

A Degenerate Operator in Non Divergence Form

2 The Fourth Order Operator if the Degeneracy Point belongs to the Boundary

3 The Domain of the Operator A and the Case x0 (0,1)

4 The General Operator of Order 2n

Korovkin Approximation of Set-Valued Integrable Functions

1 Introduction and Notation

2 Korovkin-Type Results in the Cone of Set-Valued Integrable Functions

3 Sequences of Set-Valued Kantorovich and Bernstein-Durrmeyer Operators

Convergence of a Class of Generalized Sampling Kantorovich Operators Perturbed by Multiplicative Noise

2 Notations and Preliminary Results

3 Convergence Theorems

4 Link to Classical Settings

References.

A Modification of Bernstein-Durrmeyer Operators with Jacobi Weights on the Unit Interval

3 Modified Bernstein-Durrmeyer Operators with Jacobi Weights

4 Asymptotic Formula and Its Consequences

On a Particular Scaling for the Prototype Anisotropic p-Laplacian

1 Introduction to the Problem

1.1 Structure of the Paper

2.1 Scaling Properties of Solutions

3 Scaling Invariants

4 A Topological Consequence of Energy Invariants: Lower Semi-Continuity of Super-Solutions

A Deformation Theory in Augmented Spaces and Concentration Results for NLS Equations Around Local Maxima

2 Limit Problem and Neighborhood of Expected Solutions

2.1 Limit Problems

3 -Dependent Distance and a Neighborhood of Expected Solutions

4 Concentration-Compactness Type Result

5 Tail Minimizing Vector Field

6 Deformation Argument

6.1 Deformation Result

6.2 A Special Vector Field for Deformation

7 Proof of Theorem 1.1

Some Geometric Observations on Heat Kernels of Markov Semigroups with Non-local Generators

2 Setting the Scene: The Operators (-)r and (r)

3 Some Comparisons of Semigroups

4 Two Detailed Examples and a Problem of General Nature

5 More Examples and Observations

On Oscillatory Behavior of Third Order Half-Linear Difference Equations

2 Main Results

Existence of Bounded Solutions for a Weighted Quasilinear Elliptic Equation in RN

2 Abstract Setting

3 Variational Framework and Regularity Result

4 The Main Theorem and Related Results

5 Proof of the Theorem 4.1

Elliptic and Parabolic Problems for a Bessel-Type Operator

1 Introduction.

2 The Multiplier Nλ,σ(ξ,s)=exp(-csσsrλ+ Q(ξ,r) dr)

3 The Elliptic Problem

3.1 Weighted Spaces

4 Elliptic Regularity

5 The Parabolic Problem

6 Comments on the Associated Semigroup

7 Appendix 1: A Review of Some Classic Multipliers

8 Appendix 2: The Method of Continuity

Anisotropic (p,q)-Equations with Convex and NegativeConcave Terms

3 Conditions and Hypotheses

4 Auxiliary Propositions

5 Proof of Main Theorem

5.1 Existence of Two Solutions

5.2 Existence of Third Solution

Implicit Coupled k-Generalized ψ-Hilfer Fractional Differential Systems with Terminal Conditions in Banach Spaces

3 Existence of Solutions

4 An Example

ISBN:

3-031-20021-7