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Microlocal and Time-Frequency Analysis (Hardcover): Elena Cordero, S Ivan Trapasso Microlocal and Time-Frequency Analysis (Hardcover)
Elena Cordero, S Ivan Trapasso
R1,124 R999 Discovery Miles 9 990 Save R125 (11%) Ships in 10 - 15 working days
Wave Packet Analysis of Feynman Path Integrals (Paperback, 1st ed. 2022): Fabio Nicola, S Ivan Trapasso Wave Packet Analysis of Feynman Path Integrals (Paperback, 1st ed. 2022)
Fabio Nicola, S Ivan Trapasso
R1,871 Discovery Miles 18 710 Ships in 10 - 15 working days

The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schroedinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets - can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.

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