Topic
Toeplitz operator
About: Toeplitz operator is a research topic. Over the lifetime, 1152 publications have been published within this topic receiving 13555 citations.
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1 / 2
Papers
TL;DR: In this article, the Borel sets of the unit circle in the complex plane have been normalized Lebesgue measure on the basis of φ, where φ is the eomplex conjugate of an analytic function.
Abstract: Let μ be normalized Lebesgue measure on the Borel sets of the unit circle in the complex plane. If en(z) = z for | z \\ = l and n = 0, ± l, ± 2, . . ., then the bounded measurable functions en constitute an orthonormal basis for £ = g (μ). It will be convenient to say that a function / in S (or possibly even in S) is analytic if all its Fourier coefficients with negative index vanish, i. e., if f ίβηάμ = 0 for n = — l, — 2, — 3, . . .; the eomplex conjugate of an analytic function will be called co-analytic. The analytic functions in S constitute (by definition) the class ,f); the class φ consists (by definition) of the corresponding complex conjugates.
593 citations
1 Jan 1973
400 citations
TL;DR: Brezis and Nirenberg as mentioned in this paper considered a class of maps u from a bounded domain Ω ⊂ R into R. In classical degree theory, for u ∈ C(Ω,R), the degree of u at a point
Abstract: II.0. Introduction This is a continuation of H. Brezis and L. Nirenberg [1] (= [BNI]), and we will often refer to concepts and results in that paper. There, we extended degree theory to VMO maps between compact n-dimensional oriented manifolds without boundaries. In this paper we consider a class of maps u from a bounded domain Ω ⊂ R into R. In classical degree theory, for u ∈ C(Ω,R), the degree of u at a point
333 citations
TL;DR: In this article, a sufficient condition for the product of two Toeplitz operators to be a compact perturbation of one of them is found, which is shown to be necessary under additional hypotheses.
Abstract: A sufficient condition is found for the product of two Toeplitz operators to be a compact perturbation of a Toeplitz operator The condition, which comprehends all previously known sufficient conditions, is shown to be necessary under additional hypotheses The question whether the condition is necessary in general is left open
167 citations
Posted Content•
TL;DR: In this article, it was shown that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on the boundary of the disk.
Abstract: In this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on the boundary of the disk. This result is new even when S equals a single Toeplitz operator. Our main result can be used to prove, via a unified approach, several previously known results about compact Toeplitz operators, compact Hankel operators, and appropriate products of these operators.
141 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 6 |
| 2024 | 6 |
| 2023 | 23 |
| 2022 | 42 |
| 2021 | 44 |