Mathematical Analysis, Probability and Applications – Plenary Lectures
ISAAC 2015, Macau, China

Editors: Tao Qian, Luigi G. Rodino



Offers a quick and non-technical introduction to recent major themes in analysis and its applications

Provides surveys on the latest achievements concerning partial differential equations in Mathematical Physics

Highlights outstanding mathematical schools in Asia, especially from China, Japan and Vietnam

This book collects lectures given by the plenary speakers at the 10th International ISAAC Congress, held in Macau, China in 2015. The contributions, authored by eminent specialists, present some of the most exciting recent developments in mathematical analysis, probability theory, and related applications. Topics include: partial differential equations in mathematical physics, Fourier analysis, probability and Brownian motion, numerical analysis, and reproducing kernels. The volume also presents a lecture on the visual exploration of complex functions using the domain coloring technique. Thanks to the accessible style used, readers only need a basic command of calculus.

Table of contents

Front Matter
Pages i-vii

A Review of Brownian Motion Based Solely on the Langevin Equation with White Noise
Pages 1-35

Geometry-Fitted Fourier-Mellin Transform Pairs
Pages 37-53

First Order Approach to LpLp Estimates for the Stokes Operator on Lipschitz Domains
Pages 55-75

The Study of Complex Shapes of Fluid Membranes, the Helfrich Functional and New Applications
Pages 77-101

Multiplication and Composition in Weighted Modulation Spaces
Pages 103-149

A Reproducing Kernel Theory with Some General Applications
Pages 151-182

Sparse Approximation by Greedy Algorithms
Pages 183-215

The Bi-free Extension of Free Probability
Pages 217-233

Stability of the Prandtl Boundary Layers
Pages 235-251

Visual Exploration of Complex Functions
Pages 253-279

Integral Transform Approach to Time-Dependent Partial Differential Equations
Pages 281-336

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