Results 141 to 150 of about 552 (182)

Nonlinear Riemann ‐ Hilbert Problems without Transversality

Mathematische Nachrichten, 1997
AbstractNonlinear Riemann ‐ Hilbert problems (RHP) generalize two fundamental classical problems for complex analytic functions, namely: 1. the conformal mapping problem, and 2. the linear Riemann ‐ Hilbert problem. This paper presents new results on global existence for the nonlinear (RHP) in doubly connected domains with nonclosed restriction curves ...
Efendiev, M. A., Wendland, Wolfgang L.
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ASYMPTOTIC EXPANSIONS FOR RIEMANN–HILBERT PROBLEMS

Analysis and Applications, 2008
Let Γ be a piecewise smooth contour in ℂ, which could be unbounded and may have points of self-intersection. Let V(z, N) be a 2 × 2 matrix-valued function defined on Γ, which depends on a parameter N. Consider a Riemann–Hilbert problem for a matrix-valued analytic function R(z, N) that satisfies a jump condition on the contour Γ with the jump matrix V(
Qiu, W.-Y., Wong, R.
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Riemann-Hilbert problems

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, Klaus Habetha, Wolfgang Sprößig   +2 more
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Separation Principles and Riemann-Hilbert Problems

Computational Methods and Function Theory, 2003
Let \(w_\pm\) 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, 2004
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Semmler, Gunter, Wegert, Elias
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Riemann–Hilbert Problem and Matrix Biorthogonal Polynomials

2021
Recently 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, Foulquié-Moreno, Ana, Mañas-Baena, Manuel   +2 more
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Asymptotics of oscillatory Riemann–Hilbert problems

Journal of Mathematical Physics, 1996
A 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, 2009
zbMATH 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, 2011
AbstractThis 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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The Riemann-Hilbert problem

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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