Results 101 to 110 of about 210 (150)
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Boundary Values of Holomorphic Functions and Analytic Functionals
1995The Schwarz Reflection Principle leads naturally to the consideration of boundary values of holomorphic functions. Those boundary values can exist pointwise, almost everywhere, or in some generalized sense, for instance, in the sense of distributions, as in the Edge-of-the-Wedge Theorem (see [BG, Theorem 3.6.23], [Beur]).
Carlos A. Berenstein, Roger Gay
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Analytic Description of the Spaces Dual to Spaces of Holomorphic Functions of Given Growth on Carathéodory Domains [PDF]
Mathematical Notes, 2018 The spaces dual to spaces of holomorphic functions of given growth on Caratheodory domains are described by using the Cauchy transform of functionals. A pseudoanalytic extension of such transforms to the whole plane is constructed, which makes it possible to remove convexity constrains and consider spaces determined by weights of general form, rather ...
A. V. Abanin +3 more
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Second analytic wave front set and boundary values of holomorphic functions
Applicable Analysis, 1987This paper is devoted to the study of the second analytic wave front set of boundary values of holomorphic functions. After establishing an expression of hyperfunctions without second analytic support, we give an upper bound of the second analytic wave front set of boundary values.
P. Esser, P. Laubin
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Siberian Mathematical Journal, 1989
Let \(D_{\sigma}=\{z:\) Im \(z_ j>-\sigma\), \(j=1,...,n\}\) be a product of n halfplanes. Here \(\sigma\) is a fixed positive constant. The Hardy class \(H^ 2(D_{\sigma})\) consists of such functions f holomorphic in \(D_{\sigma}\) that \[ \int_{{\mathbb{R}}\quad n}| f(x+iy)|^ 2 dx\leq c, \] where \(x=(x_ 1,...,x_ n)\), \(y=(y_ 1,...,y_ n ...
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Let \(D_{\sigma}=\{z:\) Im \(z_ j>-\sigma\), \(j=1,...,n\}\) be a product of n halfplanes. Here \(\sigma\) is a fixed positive constant. The Hardy class \(H^ 2(D_{\sigma})\) consists of such functions f holomorphic in \(D_{\sigma}\) that \[ \int_{{\mathbb{R}}\quad n}| f(x+iy)|^ 2 dx\leq c, \] where \(x=(x_ 1,...,x_ n)\), \(y=(y_ 1,...,y_ n ...
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An Algebraic Criterion for Right-Left Equivalence of Holomorphic Functions on Analytic Varieties
Bulletin of the London Mathematical Society, 1989Es werden Ergebnisse aus \textit{S. S.-T. Yau}, Proc. Symp. Pure Math. 41, 291--297 (1984; Zbl 0558.32001), verallgemeinert auf holomorphe Funktionen auf reduzierten analytischen Mengenkeimen \((X,0)\subset (\mathbb{C}^ n,0)\). Bezeichnet \(\mathcal I(X)_ 0\subset \mathcal O_{n,0}\) das Verschwindungsideal in \(\mathcal O_{n,0}\), \(\mathcal R(X ...
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Holomorphic (analytic) operators and vector-functions on complex Banach spaces
1994In Chapter I we introduced the notions of δ-differentiability, \( \mathcal{G} \)-differentiability and \( \mathcal{F} \)-differentiability of an operator \( F:\mathfrak{X} \to \mathfrak{Y} \) at a given point. For each of these notions we defined the classes of m-times differentiable operators, 1 ≤ m ≤ ∞, as well as the class of analytic operators.
David Shoiykhet, Victor Khatskevich
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ANALOGS OF DZYADYK'S THEOREM ON HOLOMORPHICITY FOR REAL ANALYTIC FUNCTIONS
Analogs of Dzyadyk’s classical theorem on the geometric description of holomorphic functions are considered. The case is investigated when the functions are real analytic in the domain, and the equality of areas is assumed only over all closed unit squares contained in the domain under consideration.Keywords: holomorphicity, Dziadyk’s theorem, PompeiusVolchkov, V. V., Timofeeva, K.V.
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Extension of bounded holomorphic functions from an analytic curve in general position to a polydisk
Functional Analysis and Its Applications, 1984Theorem: Let A be an analytic curve defined in a neighbourhood of a polydisk \(D^ n\) such that: (i) The singular points of A are situated strictly inside \(D^ n\); (ii) The intersection of A with each \(\Gamma_ i:=D_ 1\times...\times D_{i-1}\times\partial D_ i\times D_{i+1}\times...\times D_ n\) or \(\Gamma_{ij}:=\Gamma_ i\cap\Gamma_ j\) is ...
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Composition and functions of bacterial membrane vesicles
Nature Reviews Microbiology, 2023Masanori Toyofuku +2 more
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