Results 131 to 140 of about 295,436 (169)

The Corona Theorem

2001
Exercise 348. This exercise outlines another derivation of Poisson’s integral formula, based on Cauchy’s integral formula. To this end, assume first thatA; ∈ ℌ[D(0, R)] for some R > 1.
Raghavan Narasimhan, Yves Nievergelt
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Wolff’s proof of the Corona Theorem

Israel Journal of Mathematics, 1980
An expository account is given of T. Wolff’s recent elementary proof of Carleson’s Corona Theorem (1962). The Corona Theorem answers affirmatively a question raised by S. Kakatani (1957) as to whether the open unit disc in the complex plane is dense in the maximal ideal space of the Banach algebra of bounded analytic functions thereon.
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Some remarks to the corona theorem

St. Petersburg Mathematical Journal, 2013
Let \(A\) and \(B\) be Banach spaces. The space \(H^p(B)\) will denote the Hardy space of analytic functions on the unit disc taking values in \(B\), and \(H^\infty(\mathcal{L}(A,B))\) denotes the bounded analytic functions on the unit disc taking values in \(\mathcal{L}(A,B)\), the linear operators from \(A\) to \(B\).
Kislyakov, S. V., Rutsky, D. V.
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An operator corona theorem

Indiana University Mathematics Journal, 2004
Carleson's Corona theorem states that if \(F: \mathbb{D}\to\mathbb{C}^n\) is bounded and analytic on the unit disc \(\mathbb{D}\) then the Carleson condition \[ F^\ast(z) F(z)\geq \delta^2 \tag{C} \] is sufficient for the existence of a bounded analytic solution \(G\) of the Bézout equation \[ G(z)\cdot F(z)= 1\quad\text{on } \mathbb{D}.
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Factorizations, Riemann-Hilbert problems and the corona theorem

Journal of the London Mathematical Society, 2012
The solvability of the Riemann–Hilbert boundary value problem on the real line is described in the case when its matrix coefficient admits a Wiener–Hopf-type factorization with bounded outer factors, but rather general diagonal elements of its middle factor.
M. C. Câmara, Cristina Diogo, Yu. I. Karlovich, Ilya M. Spitkovsky   +3 more
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Corona theorem and interpolation

St. Petersburg Mathematical Journal, 2016
The author proves that the sequence spaces \(\ell^p\), \(1\leq p0\) with the following property: for any sequence \(\{f_k\}_k\) of functions in \( H^\infty(\mathbb{D})\) satisfying \(\delta\leq \|\{f_k(z)_k\}\|_{\ell^p}\leq 1\), \(z\in\mathbb{D}\), there is a sequence \(\{g_k\}_k\) in \(H^\infty(\mathbb{D})\) with \[ \sum_{k} f_k(z)g_k(z)=1\quad\text ...
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A Corona Theorem for Multipliers on Dirichlet Space

Integral Equations and Operator Theory, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The H p -Corona Theorem for the Polydisc

Transactions of the American Mathematical Society, 1994
Let \(H^ p\) be the Hardy space on the polydisc \(U^ n = \{z \in \mathbb{C}^ n : | z_ 1 |
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Almost periodic factorization and corona theorem

Indiana University Mathematics Journal, 1998
Using a corona theorem for classes of almost periodic matrix functions, a previously introduced transformation technique is extended to obtain almost periodic factorization for certain new classes of \(2\times 2\) block triangular matrix functions.
Rodman, Leiba, Spitkovsky, Ilya M.
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Generalized Douglas algebras and the corona theorem

Siberian Mathematical Journal, 1991
The paper deals with the structure of the maximal ideal space of generalized Douglas algebras. Given a Douglas algebra \(B\) the corresponding generalized Douglas algebra \({\mathcal H}_ B\) consists of all continuous functions on \(D=\{z\in\mathbb{C}\): \(| z|
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