Integral representations for some weighted classes of functions holomorphic in matrix domains

M. M. Djrbashian; A. H. Karapetyan

Displaying similar documents to “Integral representations for some weighted classes of functions holomorphic in matrix domains”

Envelopes of holomorphy for solutions of the Laplace and Dirac equations

Martin Kolář (1991)

Commentationes Mathematicae Universitatis Carolinae

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Analytic continuation and domains of holomorphy for solution to the complex Laplace and Dirac equations in $𝐂^{n}$ are studied. First, geometric description of envelopes of holomorphy over domains in $𝐄^{n}$ is given. In more general case, solutions can be continued by integral formulas using values on a real $n - 1$ dimensional cycle in $𝐂^{n}$ . Sufficient conditions for this being possible are formulated.

On balanced L²-domains of holomorphy

Marek Jarnicki, Peter Pflug (1996)

Annales Polonici Mathematici

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We show that any bounded balanced domain of holomorphy is an $L ²_{h}$ -domain of holomorphy.

Holomorphic functions with singularities on algebraic sets.

Sičiak, Józef (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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On certain subclasses of bounded univalent functions

J. Fuka, Z. J. Jakubowski (1991)

Annales Polonici Mathematici

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Let = z ∈ ℂ; |z| < 1, T = z ∈ ℂ; |z|=1. Denote by S the class of functions f of the form f(z) = z + a₂z² + ... holomorphic and univalent in , and by S(M), M > 1, the subclass of functions f of the family S such that |f(z)| < M in . We introduce (and investigate the basic properties of) the class S(M,m;α), 0 < m ≤ M < ∞, 0 ≤ α ≤ 1, of bounded functions f of the family S for which there exists an open $a r c I_{α} = I_{α} (f) \subset T$ of length 2πα such that ${\bar{l i m}}_{z \to z ₀, z \in} | f (z) | \leq M$ for every $z ₀ \in I_{α}$ and ${\bar{l i m}}_{z \to z ₀, z \in} | f (z) | \leq m$ for every $z ₀ \in T Ī_{α}$ .

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator $W_{k} : = Δ + \frac{k}{x_{n}} \frac{\partial}{\partial x_{n}}$ on $ℝ^{n}$ is proved. In this note there is shown that in the cases $k \neq 0$ , $k \neq 2$ no other transforms of this kind exist and for case $k = 2$ , all such transforms are described.

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and $ℤ_{p}$ the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, $k_{\infty}$ a $ℤ_{p}$ -extension of k, $k_{n}$ the nth layer of $k_{\infty} / k$ , and $A_{n}$ the p-Sylow subgroup of the ideal class group of $k_{n}$ . Iwasawa proved the following well-known theorem about the order $A_{n}$ of $A_{n}$ : Theorem A (Iwasawa). Let $k_{\infty} / k$ be a $ℤ_{p}$ -extension and $A_{n}$ the p-Sylow subgroup of the ideal class group of $k_{n}$ , where $k_{n}$ is the $n$ th layer of $k_{\infty} / k$ . Then there exist integers $λ = λ (k_{\infty} / k) \geq 0$ , $μ = μ (k_{\infty} / k) \geq 0$ , $ν = ν (k_{\infty} / k)$ , and n₀ ≥ 0...