Results 141 to 150 of about 32,369 (161)
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2016
In his famous dissertation from 1851, Bernhard Riemann (1826–1866) formulated the following problem: In a given bounded domain of the complex plane, determine a holomorphic function, if a relation is prescribed between the boundary values of its real part and its imaginary part. In the case of a linear relation this problem was first considered in 1904
Klaus Gürlebeck +2 more
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In his famous dissertation from 1851, Bernhard Riemann (1826–1866) formulated the following problem: In a given bounded domain of the complex plane, determine a holomorphic function, if a relation is prescribed between the boundary values of its real part and its imaginary part. In the case of a linear relation this problem was first considered in 1904
Klaus Gürlebeck +2 more
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Separation Principles and Riemann-Hilbert Problems
Computational Methods and Function Theory, 2003Let \(w_\pm\) be the holomorphic functions on the unit disk \(D\subset \mathbb{C}\) and let \(M_t=\{x+if(t,x)\},\;x\in R,\;t\in\partial D\) where \(f(t,x)\) is real-valued. For a given subset \(A\) in the Hardy space \(H^1\) denote by \(A_+=\{w_+\in A, v_+(t)\geq f(t,u_+(t))\;a.e.\;on\;\partial D\}\) and \(A_-=\{w_-\in A, v_-(t)\geq f(t,u_-(t))\;a.e ...
Semmler, Gunter, Wegert, Elias
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Nonlinear Riemann-Hilbert Problems and Boundary Interpolation
Computational Methods and Function Theory, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Semmler, Gunter, Wegert, Elias
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Riemann–Hilbert Problem and Matrix Biorthogonal Polynomials
2021Recently the Riemann–Hilbert problem with jumps supported on appropriate curves in the complex plane has been presented for matrix biorthogonal polynomials, in particular non–Abelian Hermite matrix biorthogonal polynomials in the real line, understood as those whose matrix of weights is a solution of a Sylvester type Pearson equation with coefficients ...
Branquinho, Amílcar +2 more
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Asymptotics of oscillatory Riemann–Hilbert problems
Journal of Mathematical Physics, 1996A classical method of stationary phase for oscillatory integrals is generalized to oscillatory Riemann–Hilbert problems of the kind arising in the theory of integrable nonlinear equations. The proposed approach is developed for the phase with N first-order stationary points, and the final formulas can immediately be applied to the problem of long-time ...
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On Riemann-Hilbert Problems in Circle Packing
Computational Methods and Function Theory, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wegert, Elias, Bauer, David
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Explicit Riemann‐Hilbert problems in Hardy spaces
Mathematische Nachrichten, 2011AbstractThis paper is concerned with boundary value problems for holomorphic functions in the unit disc, where the boundary condition is given by an explicit equation for the real and imaginary part of the solution on the unit circle. Relaxing the smoothness assumptions in well‐known results for problems of this type we can still prove the solvability ...
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2016
In Section 2.2 we have seen how important it is, at an irregular singular point, to use an appropriate formal fundamental solution to define generalized monodromy data.
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In Section 2.2 we have seen how important it is, at an irregular singular point, to use an appropriate formal fundamental solution to define generalized monodromy data.
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Riemann–Hilbert Problems on a Cut Plane
Journal of Mathematical Sciences, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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