The Cauchy Transform

By Joseph A. Cima, A. Matheson, William T. Ross. 2006

329 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/068b5f26d33bd9bf1d63d143f758fef143571f61

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In Applied Mathematics

Citations in the corpus

Integral operators mapping into the space of bounded analytic functions (2016, unknown): “where μ belongs to the space of finite complex Borel measures on T, and is endowed with the norm ‖f‖K = inf{‖μ‖ : f = Kμ} [9].”
Algebras of truncated Toeplitz operators (2010, unknown): “Note that λ is in the spectrum of Aφ if and only if infz∈D(|u(z)| + |φ(z)− λ|) = 0 [3].”
Recent Progress on Truncated Toeplitz Operators (2011, background): “dexamples of classicalextremal problems Λ(ψ) along with a computation of several extremal functions Fe. For rationalfunctions ψwith no poles on ∂D, we have seen that the linear (25) and the quadratic (26) extremal problems have the same value. Recent work of Chalendar, Fricain, and Timotin shows tha”
Detecting Confounding in Multivariate Linear Models via Spectral Analysis (2017, methodology): “To describe the relation, we first introduce Cauchy transforms [23]: Definition 6.”
Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, and Similarity (2009, background): “very Aϕ∈ TΘ is C-symmetric. Clark operators. Let us now review a few necessary facts about the theory of Clark unitary operators [5]. For a more complete account of this theory we refer the reader to [3, 19, 22]. To avoid needless technicalities, we assume that the underlying 4 J.A. CIMA, S.R. GARCI”
Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A (2015, background): “There are whole books on the Cauchy transform [38, 117].”
On the connected component of compact composition operators on the Hardy space (2007, methodology): “For the proof of this result convenient references are [6, 21], where it is established in conjunction with the classical Julia–Carathéodory theorem.”
Truncated Toeplitz Operators on Finite Dimensional Spaces (2008, background): “The operators Uα, first explored by Clark [2], have been well studied and generalized [1, 5].”
Symbols of truncated Toeplitz operators (2010, methodology): “Recall that, by a theorem of Aleksandrov, functions in K θ which are continuous in the closed disk D are dense in K θ , see [2] or [13].”