Theory of Distributions

This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This second edition, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.

Helps the reader to understand theory of distributions help students with many examples Solved problems problems with hints and problems with examples Detailed proofs of the basic facts

Autorentext

Svetlin G. Georgiev (born 1974, Bulgaria) has worked in various areas of mathematics. His current focus: harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, dynamic calculus on time scales.

Inhalt

• Introduction. - Generalities on Distributions. - Differentiation. - Homogeneous Distributions. - The Direct Product of Distributions. - Convolutions. - Tempered Distributions. - Integral Transforms. - Fundamental Solutions. - Sobolev Spaces.