Toeplitz operators on Arveson and Dirichlet spaces

Download

index.pdf

Date

2007-05-01

Author

Alpay, Daniel
Kaptanoglu, H. Turgay

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

138
views

29
downloads

We define Toeplitz operators on all Dirichlet spaces on the unit ball of C-N and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate some connections between Toeplitz and shift operators.

Subject Keywords

Algebra and Number Theory, Analysis

URI

https://hdl.handle.net/11511/65057

Journal

INTEGRAL EQUATIONS AND OPERATOR THEORY

DOI

https://doi.org/10.1007/s00020-007-1493-1

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Galois structure of modular forms of even weight Gurel, E. (Elsevier BV, 2009-10-01) We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Fibre products of Kummer covers and curves with many points Özbudak, Ferruh (Springer Science and Business Media LLC, 2007-10-01) We study the general fibre product of any two Kummer covers of the projective line over finite fields. Under some assumptions, we obtain an involved condition for the existence of rational points in the fibre product over a rational point of the projective line so that we determine the exact number of the rational points. Using this, we construct explicit examples of such fibre products with many rational points. In particular we obtain a record and a new entry for the table (http://www.science.uva.nl/(simi...
Value sets of Lattes maps over finite fields Küçüksakallı, Ömer (Elsevier BV, 2014-10-01) We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
Curves with many points and configurations of hyperplanes over finite fields Özbudak, Ferruh (Elsevier BV, 1999-10-01) We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterle bound. (C) 1999 Academic Press.
On the deformation chirality of real cubic fourfolds Finashin, Sergey (Wiley, 2009-09-01) According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...

Citation Formats

D. Alpay and H. T. Kaptanoglu, “Toeplitz operators on Arveson and Dirichlet spaces,” INTEGRAL EQUATIONS AND OPERATOR THEORY, pp. 1–33, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65057.