The Uncertainty Principle in Harmonic Analysis: 28 (Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics) - Hardcover

Khavin, Viktor Petrovich; Joricke, Burglind

Hardcover

ISBN 10: 354056991X ISBN 13: 9783540569916

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1994

Synopsis

The present book is a collection of variations on a theme which can be summed up as follows: It is impossible for a non-zero function and its Fourier transform to be simultaneously very small. In other words, the approximate equalities x :::::: y and x :::::: fj cannot hold, at the same time and with a high degree of accuracy, unless the functions x and yare identical. Any information gained about x (in the form of a good approximation y) has to be paid for by a corresponding loss of control on x, and vice versa. Such is, roughly speaking, the import of the Uncertainty Principle (or UP for short) referred to in the title ofthis book. That principle has an unmistakable kinship with its namesake in physics - Heisenberg's famous Uncertainty Principle - and may indeed be regarded as providing one of mathematical interpretations for the latter. But we mention these links with Quantum Mechanics and other connections with physics and engineering only for their inspirational value, and hasten to reassure the reader that at no point in this book will he be led beyond the world of purely mathematical facts. Actually, the portion of this world charted in our book is sufficiently vast, even though we confine ourselves to trigonometric Fourier series and integrals (so that "The U. P. in Fourier Analysis" might be a slightly more appropriate title than the one we chose).

About this title

Synopsis

Devoted to the uncertainty principle (UP), this volume contains a collection of essays dealing with the various manifestations of this phenomenon. The authors describe different approaches to the subject, using both "real" and "complex" techniques and show the influence of the UP in areas outside Fourier analysis. The book is essentially self-contained and thus accessible to any graduate student acquainted with the fundamentals of Fourier, complex and functional analysis.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1994
• Language: English
• ISBN 10: 354056991X
• ISBN 13: 9783540569916
• Binding: Hardcover
• Number of pages: 559