A Bochner-Martinelli formula for vector fields which satisfy the generalized Cauchy-Riemann equations
R. G. M. Brummelhuis (1988)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Displaying similar documents to “The N-Dimensional Cauchy-Riemann equations.”
A Bochner-Martinelli formula for vector fields which satisfy the generalized Cauchy-Riemann equations
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M.-C. Shaw (1985)
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The Riemann problem has been solved in [9] for an arbitrary closed Riemann surface in terms of the principal functionals. This paper is devoted to solution of the problem only for the double of a multiply connected region and can be treated as complementary to [9,1]. We obtain a complete solution of the Riemann problem in that particular case. The solution is given in analytic form by a Poincaré series.
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Begehr, Heinrich (1997)
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Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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In this paper, we shall estimate the growth order of the n-th derivative Cauchy integrals at a point in terms of the distance between the point and the boundary of the domain. By using the estimate, we shall generalize Plemelj–Sokthoski theorem. We also consider the boundary behavior of generalized Cauchy integrals on compact bordered Riemann surfaces.
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László Lempert (1994)
Mathematische Annalen
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Riemann mapping theorem in ℂⁿ
Krzysztof Jarosz (2012)
Annales Polonici Mathematici
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The classical Riemann Mapping Theorem states that a nontrivial simply connected domain Ω in ℂ is holomorphically homeomorphic to the open unit disc 𝔻. We also know that "similar" one-dimensional Riemann surfaces are "almost" holomorphically equivalent. We discuss the same problem concerning "similar" domains in ℂⁿ in an attempt to find a multidimensional quantitative version of the Riemann Mapping Theorem
The Cauchy Kernel, the Szegö Kernel, and the Riemann Mapping Function.
N. Kerzman, E.M. Stein (1978)
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On the Maximum Modulus Principle for the Tangential Cauchy-Riemann Equations.
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We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.
Variation of the argument of the Riemann ξ function on vertical lines
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Obolashvili, E. (1997)
Memoirs on Differential Equations and Mathematical Physics
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