Introduction to the Uncertainty Principle (e-bog) af Thangavelu, Sundaram
Thangavelu, Sundaram (forfatter)

Introduction to the Uncertainty Principle e-bog

436,85 DKK (inkl. moms 546,06 DKK)
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer- sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark o...
E-bog 436,85 DKK
Forfattere Thangavelu, Sundaram (forfatter)
Forlag Birkhauser
Udgivet 6 december 2012
Genrer PBKD
Sprog English
Format pdf
Beskyttelse LCP
ISBN 9780817681647
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer- sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "e;a f and g [= j] cannot both be very small"e;. ... The theo- pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.