Mathematics Past and Present Fourier Integral Operators

ISBN-13: 9783642081590 / Angielski / Miękka / 2010 / 288 str.

Jochen Bruning; Victor W. Guillemin; J. J. Duistermaat

Opis

What is the true mark of inspiration? Ideally it may mean the originality, freshness and enthusiasm of a new breakthrough in mathematical thought. The reader will feel this inspiration in all four seminal papers by Duistermaat, Guillemin and Hormander presented here for the first time ever in one volume. However, as time goes by, the price researchers have to pay is to sacrifice simplicity for the sake of a higher degree of abstraction. Thus the original idea will only be a foundation on which more and more abstract theories are being built. It is the unique feature of this book to combine the basic motivations and ideas of the early sources with knowledgeable and lucid expositions on the present state of Fourier Integral Operators, thus bridging the gap between the past and present. A handy and useful introduction that will serve novices in this field and working mathematicians equally well."

Spis treści

25 Years of Fourier Integral Operators.- Fourier Integral Operators. I.- Fourier Integral Operators. II.- The Spectral Function of an Elliptic Operator.- The Spectrum of Positive Elliptic Operators and Periodic Bicharacteristics.

O autorze

The reader will feel the inspiration, freshness and enthusiasm of a new breakthrough in mathematical thought in the 4 seminal papers presented here for the first time ever in one volume. The 4 papers by Duistermaat, Guillemin and Hörmander have been a milestone in the development of this field. The new ideas presented in these papers - in a very lucid and accessible form - became the foundation on which more and more abstract theories were built in the relentless march towards even better and more detailed results. The detailed introductory comments by V. Guillemin are the final touch in a volume that combines the basic motivation and ideas of the early sources with the present state of F.I.O. thus bridging the gap between the past and present.