Results 81 to 90 of about 11,899 (141)

Fractional Inner Products and Orthogonal Polynomial Structures: A Riemann-Liouville Framework for Spectral Approximation

Axioms
This paper develops an operator-oriented framework for spectral approximation in fractional calculus by introducing a fractional inner product defined through the Riemann-Liouville integral. Instead of modifying polynomial families, the proposed approach
Muath Awadalla, Dalal Alhwikem
doaj   +1 more source

Brussels-Austin Nonequilibrium Statistical Mechanics in the Later Years: Large Poincaré Systems and Rigged Hilbert Space [PDF]

, 2003
This second part of a two-part essay discusses recent developments in the Brussels-Austin Group after the mid 1980s. The fundamental concerns are the same as in their similarity transformation approach (see Part I), but the contemporary approach utilizes
Bishop, Robert
core  

Riemann-Hilbert problems, Toeplitz operators and ergosurfaces

Journal of High Energy Physics
The Riemann-Hilbert approach, in conjunction with the canonical Wiener-Hopf factorisation of certain matrix functions called monodromy matrices, enables one to obtain explicit solutions to the non-linear field equations of some gravitational theories ...
M. Cristina Câmara, Gabriel Lopes Cardoso   +1 more
doaj   +1 more source

THE RIEMANN–HILBERT APPROACH TO GLOBAL ASYMPTOTICS OF DISCRETE ORTHOGONAL POLYNOMIALS WITH INFINITE NODES

, 2010
In this paper, we develop the Riemann–Hilbert approach to study the global asymptotics of discrete orthogonal polynomials with infinite nodes. We illustrate our method by concentrating on the Charlier polynomials [Formula: see text].
CHUNHUA OU, R. WONG
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Emergent Random Matrix Universality in Quantum Operator Dynamics

Physical Review X
The high complexity of many-body quantum dynamics means that essentially all analytical or numerical approaches either exploit special structure or are approximate in nature.
Oliver Lunt, Thomas Kriecherbauer, Kenneth T-R McLaughlin, Curt von Keyserlingk   +3 more
doaj   +1 more source

Response of a strip grating on a ferromagnetic half-space: A Riemann-Hilbert approach

, 2010
The problem of diffraction of electromagnetic plane waves from a perfectly conducting periodic strip grating is solved when the grating lies at the half-space interface between a lossy ferromagnetic medium and free space. Rigorous solution is obtained by
A. Troshilo, Melejik, P, E. Vinogradova, A. Poedinchuk, Poedinchuk, A, P. Melejik, Vynogradova, Olena, A. Brovenko, Brovenko, A, Troshilo, A   +9 more
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Initial and boundary value problems in two and three dimensions

, 2010
This thesis: (a) presents the solution of several boundary value problems (BVPs) for the Laplace and the modified Helmholtz equations in the interior of an equilateral triangle; (b) presents the solution of the heat equation in the interior of an ...

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The Riemann-Hilbert problem approach to the short pulse equation

, 2022
We consider the adaptation of the inverse scattering transform method, in the form of a Riemann-Hilbert factorization problem, to the study of the Cauchy problem for the shortpulse equation u_xt = u + (1/6)(u^3)_ xx. It is shown that the solution of this
Zielinski, Lech, Tiurdio, A, Shepelsky, D   +2 more
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On tau functions associated with linear systems [PDF]

, 2012
\noindent {\bf Abstract} This paper considers the Fredholm determinant $\det (I-\Gamma_x)$ of a Hankel integral operator on $L^2(0, \infty )$ with kernel $\phi (s+t+2x)$, where $\phi$ is a matrix scattering function.
Samantha L. Newsham, Gordon Blower, Newsham, Samantha, Blower, Gordon   +3 more
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Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight

We describe methods for the derivation of strong asymptotics for the denominator polynomials and the remainder of Pade approximants for a Markov function with a complex and varying weight.
A. I. Aptekarev, W. Van Assche
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