Math 247a - Harmonic Analysis

Lecture Notes 1 for 247a

The aim of this course is to introduce the basic tools and theory of real-variable harmonic analysis very roughly speaking, the art of estimating the size of an output function in terms of the size of an input function, when a known transformation (linear, multilinear, or nonlinear) is applied. In particular we shall focus on the classical Calderón-Zygmund-Stein theory, in which we study such o...

A new class of Salagean-type harmonic univalent functions

and Applied Analysis 3 2. Preliminaries A continuous function f u iv is a complex-valued harmonic function in a domain D ⊂ if both u and v are real harmonic in D. In any simply connected domain, we can write

Solving the Laplace equation by meshless collocation using harmonic kernels

We present a meshless technique which can be seen as an alternative to the Method of Fundamental Solutions (MFS). It calculates homogeneous solutions of the Laplacian (i.e. harmonic functions) for given boundary data by a direct collocation technique on the boundary using kernels which are harmonic in two variables. In contrast to the MFS, there is no artifical boundary needed, and there is a f...

Solving Time-Harmonic Scattering Problems Based on the Pole Condition I: Theory

Solving Time-Harmonic Scattering Problems Based on the Pole Condition II: Convergence of the PML Method