Mathematical analysis, probability and applications - plenary lectures : ISAAC 2015, Macau, China

Description

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 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 \(L^p\) 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