Fourier Analysis and Distributions

Rolf Brigola studied and received his doctorate in mathematics at the University of Erlangen-Nürnberg, Germany. and was research assistent in the faculty of mathematics at the University of Regensburg, Germany, in the fields of functional analysis and stochastic processes. He has more than 10 years work experience in development and application of mathematical methods (electrodynamics, control engineering, elasticity problems) in the energy technology division of Siemens AG in Erlangen and in development of operating system and application software for digital communication systems in the communications technology division of Siemens AG in Munich, Germany. Since 1988 he has worked as professor for mathematics with students of applied mathematics, physics and engineering disciplines. He is the author of the previous textbook "Fourieranalysis, Distributionen und Anwendungen" in German with Vieweg in 1996.

• Preface.- Introduction.- Trigonometric Polynomials, Fourier Coefficients.- Fourier Series.- Calculating with Fourier Series.- Application Examples for Fourier Series.- Discrete Fourier Transforms, First Applications.- Convergence of Fourier Series.- Fundamentals of Distribution Theory.- Application Examples for Distributions.- The Fourier Transform.- Basics of Linear Filters.- Further Applications of the Fourier Transform.- The Malgrange-Ehrenpreis Theorem.- Outlook on Further Concepts.- A The Residue Theorem and the Fundamental Theorem of Algebra.- B Tools from Integration Theory.- C Solutions to the Exercises.- References.- List of Symbols and Physical Quantities.- Index.