Download Bergman Spaces and Related Topics in Complex Analysis: by Hadenmalm & Zhu Borichev PDF

By Hadenmalm & Zhu Borichev

This quantity grew out of a convention in honor of Boris Korenblum at the social gathering of his eightieth birthday, held in Barcelona, Spain, November 20-22, 2003. The publication is of curiosity to researchers and graduate scholars operating within the idea of areas of analytic functionality, and, specifically, within the idea of Bergman areas. This booklet is copublished with Bar-Ilan collage (Ramat-Gan, Israel)

Show description

Read or Download Bergman Spaces and Related Topics in Complex Analysis: Proceedings of a Conference in Honor of Boris Korenblum's 80th Birthday, November 20-23, 2003 PDF

Similar functional analysis books

Ginzburg-Landau Vortices

The Ginzburg-Landau equation as a mathematical version of superconductors has develop into a really useful gizmo in lots of components of physics the place vortices wearing a topological cost seem. The impressive growth within the mathematical knowing of this equation consists of a mixed use of mathematical instruments from many branches of arithmetic.

Mathematical analysis

The aim of the quantity is to supply a aid for a primary direction in Mathematical research, alongside the strains of the hot Programme requirements for mathematical educating in ecu universities. The contents are organised to charm specifically to Engineering, Physics and desktop technological know-how scholars, all components within which mathematical instruments play a vital function.

Sobolev inequalities, heat kernels under Ricci flow, and the Poincare conjecture

Concentrating on Sobolev inequalities and their functions to research on manifolds and Ricci circulation, Sobolev Inequalities, warmth Kernels below Ricci movement, and the Poincaré Conjecture introduces the sector of study on Riemann manifolds and makes use of the instruments of Sobolev imbedding and warmth kernel estimates to check Ricci flows, in particular with surgical procedures.

Additional info for Bergman Spaces and Related Topics in Complex Analysis: Proceedings of a Conference in Honor of Boris Korenblum's 80th Birthday, November 20-23, 2003

Example text

Then Hp (Rn ) = {f ∈ S � (Rn ): �f ∗ | Lp � < ∞} (3) f ∗ (x) = sup |ϕ(tD)f (y)| (4) with |x−y|0 (5) Remark 1. A proof of this crucial theorem may be found in [FeS2: Theorem 11]. 2/7) we have the extension f → ϕ(tD)f (x) and (4). The harmonic extension can be recovered if one chooses ϕ(ξ) = e−|ξ| (which is not smooth at the origin, 2 but this is unimportant). , n+1 ϕ(tD)f (x) obeys the heat equation in R+ . We return to this subject later on in connection with characterizations of function spaces in terms of Gauss–Weierstrass and Cauchy–Poisson semi-groups.

Krejn and N. Aronszajn. Comprehensive treatments of interpolation theory, including many historical references, may be found in [BeL, Triα, KPS, BKS]. The dominating figure in interpolation theory in the sixties and early seventies was J. Peetre. In particular, he created the so-called K-functional which is the crucial instrument in real interpolation up to our time. At the beginning, in the early sixties, abstract interpolation theory was closely connected with PDE’s and function spaces. Even more, applications to PDE’s and function spaces were the motivating force behind interpolation theory at this stage of the theory.

1. How to measure smoothness 52 Remark 2. The above theorem and the assertions of the last subsections show s s that some spaces Fpq and Bpq and all spaces Lsp and Cps can be based on the same principle: measurement of smoothness via approximation by algebraic polynomials. The restriction of this procedure to Rn or to bounded C ∞ domains is not necessary. Just on the contrary, one can use these methods in order to introduce and study, say, spaces of Besov type on arbitrary non-smooth sets. We refer to this connection to [JoW, Wal] and the papers mentioned there.

Download PDF sample

Rated 4.01 of 5 – based on 15 votes