Recent Advances in Mathematical Analysis: Celebrating the 70th Anniversary of Francesco Altomare

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
1 Introduction
2 A Conjecture
3 A Result Related to the Conjecture
References
A Strong Variant of Weyl's Theorem Under Functional Calculus and Perturbations
1 Introduction
2 Definitions and Preliminary Results
3 S-Weyl's Theorem
4 S-Weyl's Theorem Under Commuting Perturbations
References
Multiplication and Convolution Topological Algebras in Spaces of ω-Ultradifferentiable Functions of Beurling Type
1 Introduction
2 Definitions and Preliminary Results
3 The Algebras (OM,ω(RN),·), (Sω(RN),·), (Sω(RN),) and (OC,ω(RN),)
4 Hypocontinuity and Discontinuity
4.1 Hypocontinuity
4.2 Discontinuity
References
Higher Order Elliptic Equations in Generalized Morrey Spaces
1 Introduction
2 Definitions and Preliminary Results
3 Statement of the Problem and the Main Result
References
Norm and Essential Norm of Composition Operators Mapping into Weighted Banach Spaces of Harmonic Mappings
1 Introduction
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
References
Generalized Gaussian Estimates for Elliptic Operators with Unbounded Coefficients on Domains
1 Introduction
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
References
An Existence Result for Perturbed (p,q)-Quasilinear EllipticProblems
1 Introduction
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
References
Weighted Composition Operators on Weighted Spaces of Banach Valued Analytic Functions
1 Introduction
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
References
Existence of Positive Solutions of Nonlinear Second Order Dirichlet Problems Perturbed by Integral Boundary Conditions
1 Introduction
2 Linear Part: Green's Function
2.1 Case γ=0
2.2 Case γ>0
2.3 Case γ<0
3 Nonlinear Problem
3.1 Problem (2), (3)
References
A Degenerate Operator in Non Divergence Form
1 Introduction
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
References
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
References
Convergence of a Class of Generalized Sampling Kantorovich Operators Perturbed by Multiplicative Noise
1 Introduction
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
1 Introduction
2 Preliminaries
3 Modified Bernstein-Durrmeyer Operators with Jacobi Weights
4 Asymptotic Formula and Its Consequences
References
On a Particular Scaling for the Prototype Anisotropic p-Laplacian
1 Introduction to the Problem
1.1 Structure of the Paper
2 Preliminaries
2.1 Scaling Properties of Solutions
3 Scaling Invariants
4 A Topological Consequence of Energy Invariants: Lower Semi-Continuity of Super-Solutions
References
A Deformation Theory in Augmented Spaces and Concentration Results for NLS Equations Around Local Maxima
1 Introduction
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
References
Some Geometric Observations on Heat Kernels of Markov Semigroups with Non-local Generators
1 Introduction
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
References
On Oscillatory Behavior of Third Order Half-Linear Difference Equations
1 Introduction
2 Main Results
References
Existence of Bounded Solutions for a Weighted Quasilinear Elliptic Equation in RN
1 Introduction
2 Abstract Setting
3 Variational Framework and Regularity Result
4 The Main Theorem and Related Results
5 Proof of the Theorem 4.1
References
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
References
Anisotropic (p,q)-Equations with Convex and NegativeConcave Terms
1 Introduction
2 Preliminaries
3 Conditions and Hypotheses
4 Auxiliary Propositions
5 Proof of Main Theorem
5.1 Existence of Two Solutions
5.2 Existence of Third Solution
References
Implicit Coupled k-Generalized ψ-Hilfer Fractional Differential Systems with Terminal Conditions in Banach Spaces
1 Introduction
2 Preliminaries
3 Existence of Solutions
4 An Example
References