Download e-book for iPad: Analysis on Fock Spaces by Kehe Zhu (auth.)

Posted by

By Kehe Zhu (auth.)

ISBN-10: 1441988009

ISBN-13: 9781441988003

Several normal Lp areas of analytic capabilities were extensively studied some time past few a long time, together with Hardy areas, Bergman areas, and Fock areas. The phrases “Hardy areas” and “Bergman areas” are by means of now ordinary and good confirmed. however the time period “Fock areas” is a special story.

Numerous very good books now exist with reference to Hardy areas. numerous books approximately Bergman areas, together with many of the author’s, have additionally seemed long ago few many years. yet there was no booklet out there in regards to the Fock areas. the aim of this publication is to fill that void, specially while many ends up in the topic are whole by means of now. This e-book provides vital effects and methods summarized in a single position, in order that new comers, particularly graduate scholars, have a handy connection with the subject.

This e-book comprises proofs which are new and easier than the prevailing ones within the literature. specifically, the booklet avoids using the Heisenberg crew, the Fourier remodel, and the warmth equation. this assists in keeping the must haves to a minimal. a regular graduate path in every one of actual research, advanced research, and useful research will be adequate guidance for the reader.

Show description

Read Online or Download Analysis on Fock Spaces PDF

Similar quantum theory books

Mikio Nakahara, Robabeh Rahimi, Akira Saitoh's Mathematical Aspects of Quantum Computing 2007 PDF

This ebook presents a accomplished evaluate of the mathematical facets of quantum computing. it will likely be beneficial for graduate scholars and researchers attracted to quantum computing from assorted parts of physics, arithmetic, informatics and machine technological know-how. The lecture notes during this quantity are written in a self-contained sort, and consequently are available for graduate scholars and researchers with even much less historical past within the themes.

Read e-book online Fourth Summer School in Analysis and Mathematical Physics: PDF

This e-book involves 3 expository articles written via awesome researchers in Mathematical Physics: Rafael Benguria, Peter Hislop, and Elliott Lieb. The articles are in line with their lectures on the Fourth summer time tuition in research and Mathematical Physics, held on the Institute of arithmetic, Universidad Nacional Autonoma de Mexico, Cuernavaca in might 2005.

Additional info for Analysis on Fock Spaces

Sample text

Since the polynomials are dense in Fαp , we have proved the result for Fαp , 0 < p < ∞. The proof for fα∞ is similar. Finally, in this section, as a consequence of the pointwise estimates, we establish the maximum order and type for functions in the Fock spaces. 12. Let f ∈ Fαp with 0 < p ≤ ∞. Then f is of order less than or equal to 2. When f is of order 2, it must be of type less than or equal to α /2. Proof. 8, there exists a positive constant C such that | f (z)| ≤ Ceα |z| 2 /2 42 2 Fock Spaces for all z ∈ C.

Therefore, we have α = 2β . 18. Suppose 1 < p ≤ 2 and Pα is bounded on L p (C, dλβ ). Then pα = 2β . Proof. Once again, we consider functions of the form fx,k (z) = e−x|z| zk , 2 z ∈ C, where x > 0 and k is a positive integer. 2 Some Integral Operators 47 = α (β −α )|z|2 e β +x = α (β −α )|z|2 e β +x α β +x = 1+k C e(β +x)[α z/(β +x)]w¯ wk dλβ +x(w) αz β +x k e(β −α )|z| zk . 2 Suppose 1 < p ≤ 2 and 1/p + 1/q = 1. If the operator Pα is bounded on L p (C, dλβ ), then the operator Pα∗ is bounded on Lq (C, dλβ ).

21). Details are left to the reader. 28. We have ρ (p1 , q1 )ρ (p2 , q2 ) = e2α i(p1 q2 −p2 q1 ) ρ (p2 , q2 )ρ (p1 , q1 ) for all real numbers p1 , q1 , p2 , and q2 . Proof. 27. 29. Suppose α is any positive parameter and pseudodifferential operators are defined as in the previous section. For any real p and q, the pseudodif- 26 1 Preliminaries ferential operator e2α i(pD+qX) is a unitary operator on L2 (R, dx). Furthermore, the mapping (p + iq,t) → u(p + iq,t) =: eα it e2α i(pD+qX) is a unitary representation of the Heisenberg group H on L2 (R, dx).

Download PDF sample

Analysis on Fock Spaces by Kehe Zhu (auth.)

by Charles

Rated 4.02 of 5 – based on 47 votes