An Introduction to the Uncertainty Principle: Hardy’s - download pdf or read online

By Sundaram Thangavelu

ISBN-10: 0817643303

ISBN-13: 9780817643300

ISBN-10: 1461264685

ISBN-13: 9781461264682

In 1932 Norbert Wiener gave a chain of lectures on Fourier research on the Univer­ sity of Cambridge. One results of Wiener's stopover at to Cambridge used to be his recognized textual content The Fourier essential and sure of its functions; one other was once a paper by way of G. H. Hardy within the 1933 Journalofthe London Mathematical Society. As Hardy says within the advent to this paper, This be aware originates from a comment of Prof. N. Wiener, to the impact that "a f and g [= j] can't either be very small". ... The theo­ pair of transforms rems which stick with provide the main specific interpretation attainable ofWiener's comment. Hardy's personal assertion of his effects, calmly paraphrased, is as follows, during which f is an integrable functionality at the genuine line and f is its Fourier remodel: x 2 m If f and j are either zero (Ix1e- /2) for big x and a few m, then every one is a finite linear mixture ofHermite features. specifically, if f and j are x2 x 2 2 2 either O(e- / ), then f = j = Ae- / , the place A is a continuing; and if one x 2 2 is0(e- / ), then either are null.

Show description

Read or Download An Introduction to the Uncertainty Principle: Hardy’s Theorem on Lie Groups (Progress in Mathematics) PDF

Best functional analysis books

J. Dieudonne's History of Functional Analysis (North-Holland Mathematics PDF

Background of practical research offers sensible research as a slightly complicated mixture of algebra and topology, with its evolution encouraged by way of the advance of those branches of arithmetic. The publication adopts a narrower definition—one that's assumed to meet quite a few algebraic and topological stipulations.

T. Aoki,H. Majima,Y. Takei,N. Tose's Algebraic Analysis of Differential Equations: from PDF

This quantity comprises 23 articles on algebraic research of differential equations and similar subject matters, so much of which have been offered as papers on the convention "Algebraic research of Differential Equations – from Microlocal research to Exponential Asymptotics" at Kyoto college in 2005. This quantity is devoted to Professor Takahiro Kawai, who's one of many creators of microlocal research and who brought the means of microlocal research into exponential asymptotics.

New PDF release: Vladimir I. Arnold - Collected Works: Hydrodynamics,

Vladimir Arnold used to be one of many nice mathematical scientists of our time. he's recognized for either the breadth and the intensity of his paintings. even as he's essentially the most prolific and remarkable mathematical authors. This moment quantity of his accumulated Works makes a speciality of hydrodynamics, bifurcation concept, and algebraic geometry.

Boris Zacharowitsch Wulich,Martin R. Weber's Geometrie der Kegel: In normierten Räumen (De Gruyter PDF

Aufbauend auf Grundkenntnissen der research und der linearen Algebra behandelt dieses Lehrbuch die Geometrie der Kegel in geordneten normierten Räumen. Einerseits werden grundlegende Konzepte wie geordnete Vektorräume erläutert, andererseits werden – Grundkenntnisse in der Funktionalanalysis vorausgesetzt – Eigenschaften von Kegeln und deren dualen Kegeln in normierten Räumen systematisch untersucht sowie Kegel im Raum der linearen stetigen Operatoren behandelt.

Extra info for An Introduction to the Uncertainty Principle: Hardy’s Theorem on Lie Groups (Progress in Mathematics)

Sample text

Download PDF sample

An Introduction to the Uncertainty Principle: Hardy’s Theorem on Lie Groups (Progress in Mathematics) by Sundaram Thangavelu

by James

Rated 4.38 of 5 – based on 7 votes

About the Author