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

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