دانلود کتاب Analysis and Partial Differential Equations: Perspectives from Developing Countries: Imperial College London, UK, 2016

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Preface
Contents
Contributors
Analysis in Developing Countries
Francis K. A. Allotey (Saltpond, Ghana 9 August 1932 – Accra, Ghana 2 November 2017)
1 Francis Kofi Ampenyin Allotey
State of Mathematics in Africa and the Way Forward
1 Introduction
2 Levels of Research
3 The Gender Question
4 Capacity Building
5 Academic Exchange Programmes
6 Benefits of Research Cooperation
7 Some Centres of Excellence and Networks in Mathematical Sciences in Africa
8 The Way forward
The Optimal Vector Control for the Elastic Oscillations Described by Fredholm Integral-Differential Equations
1 Introduction
2 Boundary Value Problem of the Controlled Process
3 Formulation of Optimal Control Problem and Conditions Optimality
4 Solution of the Conjugate Boundary Value Problem
5 System of Nonlinear Integral Equations of the Optimal Vector Control
6 Conclusion
References
On Nuclear Lp-Multipliers Associated to the Harmonic Oscillator
1 Introduction
2 r-Nuclear Multipliers Associated to the Harmonic Oscillator
2.1 Preliminaries and Notations: Nuclear Operators on Lebesgue Spaces
2.2 Nuclear Multipliers of the Harmonic Oscillator
3 Spectral and Nuclear Traces of Multipliers of the Harmonic Oscillator
3.1 Trace Formulae for Multipliers
3.2 The Hermite Semigroup
References
Hermite Multipliers on Modulation Spaces
1 Introduction
2 Notation and Preliminaries
2.1 Notations
2.2 Heisenberg Group and Fourier Multipliers
2.3 Hermite and Special Hermite Functions
2.4 A Transference Theorem for m(L)
2.5 Modulation Spaces
3 Hermite Multipliers via Transference Theorems
4 Hermite Multipliers via Fourier Multipliers on Torus
5 Hermite Multiplier for Schrödinger Propagator
References
Potential Theory Results for a Class of PDOs Admitting a Global Fundamental Solution
1 Introduction
2 A Non-invariant Harnack Inequality
3 Further Potential Theory Results
4 An Invariant Harnack Inequality
5 The Existence of the Fundamental Solution for a Class of PDOs
References
Semiclassical Analysis of Dispersion Phenomena
1 Introduction
1.1 Description of the Problem
1.2 Non Dispersive Effects Associated to Isolated Critical Points
1.3 Non Dispersive Effects Associated to a Manifold of Critical Points
1.4 Link with Smoothing-Type Estimates
2 The Microlocal Approach to the Problem
2.1 Wigner Measures
2.2 Two-Microlocal Wigner Measures
3 The Particular Case: Countable Critical Points
3.1 Two Microlocal Wigner Measures Associated to a Critical Point
3.2 Degenerate Critical Points
4 Some Comments on the Case of a Manifold of Critical Points
References
Convergence of Fourier-Walsh Double Series in Weighted Lp[0,1)2
1 Introduction
2 Proofs of the Main Lemmas
3 Proof of Theorem 5
References
``Strong\'\' Turing-Hopf Instability for Reaction-Diffusion Systems
1 Introduction
2 Preliminaries
3 Strong Turing-Hopf instabilities to the glycolysis system
4 Strong Turing-Hopf instability to the Lengyel-Epstein system
5 Conclusions
References
Correspondence Between Multiscale Frame Shrinkage and High-Order Nonlinear Diffusion
1 Introduction
2 Frame Shrinkage at Different scales
3 High-Order Nonlinear Diffusion Equation
4 The Correspondence Between General Frame Shrinkage and High-Order Nonlinear Diffusion
5 Application to Axial-flow Compressor
6 Conclusion and Future Work
References
Pseudo-differential Operators Associated to General Type I Locally Compact Groups
1 Introduction
2 General Type I Locally Compact Groups
3 The Fourier and Plancherel Transforms
4 The Basic Quantization
5 Other Quantizations
6 Some Operators Arising from the Calculus
7 The C*-Algebraic Formalism
8 The Case of Exponential Lie Groups
9 The Affine Group
References
Existence and Numerical Computation of Standing Wave Solutions for a System of Two Coupled Schrödinger Equations
1 Introduction
2 Preliminaries
3 Existence of Standing Wave Solutions
4 Numerical results
5 Conclusions
References
Shannon Sampling and Weak Weyl\'s Law on Compact Riemannian Manifolds
1 Introduction
1.1 Objectives
1.2 Weyl\'s Asymptotic Formula on Compact Riemannian Manifolds
2 Covering Lemma
3 Sampling Sets for Bandlimited Functions and the Upper Estimate on the Number of Eigenvalues
3.1 Poincare-Type Inequality on Manifolds
3.2 Sampling Sets for Bandlimited Functions and the Upper Estimate on the Number of Eigenvalues
4 The Lower Estimate
4.1 Kernels on Compact Riemannian Manifolds
4.2 The Lower Estimate
References
Well-posed Boundary Value Problems for New Classes of Singular Integral Equations in Cylindrical Domains
1 Introduction
1.1 Determination of Solution of Integral Equation (1), in the Case, When Coefficients are Disconnected Among Themselves
2 Dirichlet Type Problem
References
Weighted Stepanov-Like Pseudo Almost Automorphic Solutions of Class r for Some Partial Differential Equations
1 Introduction
2 Variation of Constants Formula and Spectral Decomposition
3 Almost Automorphic Functions and (,) Ergodic Functions
4 (,)-Stepanov-Like Pseudo Almost Periodic Functions
5 Properties of -Stepanov-Like Pseudo Almost Automorphic Functions of Class r
6 Weighted Stepanov Like Pseudo Almost Automorphic Solutions of Class r
7 Application
References