Results 21 to 30 of about 87 (84)
Heisenberg‐smooth operators from the phase‐space perspective
Mathematische Nachrichten, Volume 298, Issue 8, Page 2845-2866, August 2025.Abstract Cordes' characterization of Heisenberg‐smooth operators bridges a gap between the theory of pseudo‐differential operators and quantum harmonic analysis (QHA). We give a new proof of the result by using the phase‐space formalism of QHA. Our argument is flexible enough to generalize Cordes' result in several directions: (1) we can admit general ...
Robert Fulsche, Lauritz van Luijk
wiley +1 more source
On the wave turbulence theory of 2D gravity waves, I: Deterministic energy estimates
Communications on Pure and Applied Mathematics, Volume 78, Issue 2, Page 211-322, February 2025.Abstract Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV‐type equations. However, our situation
Yu Deng +2 more
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Numerical Approaches in Nonlinear Fourier Transform‐Based Signal Processing for Telecommunications
Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.ABSTRACT We discuss applications of the inverse scattering transform, also known as the nonlinear Fourier transform (NFT) in telecommunications, both for nonlinear optical fiber communication channel equalization and time‐domain signal processing techniques.
Egor Sedov +3 more
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Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.The Kadomtsev–Petviashvili (KP) equation and the Bogoyavlensky–Konopelchenko (BK) equation are fundamental models in the study of nonlinear wave dynamics, describing the evolution of weakly dispersive, quasi‐two‐dimensional (2D) wave phenomena in integrable systems.
Md. Abdul Aziz, Jingli Ren
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Infinite dimensional weak Dirichlet processes, stochastic PDEs and optimal control [PDF]
, 2012 The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context.
RUSSO, Francesco +3 more
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, 2021 The present thesis deals with non Markovian linear-quadratic stochastic control problems. It is divided into three parts. In the first part, we tackle stochastic Volterra control problems whose kernel can be expressed as Laplace transform.
Miller, Enzo
core
Hypercomplex operator calculus for the fractional Helmholtz equation
Mathematical Methods in the Applied Sciences, Volume 47, Issue 14, Page 11439-11472, 30 September 2024.In this paper, we develop a hypercomplex operator calculus to treat fully analytically boundary value problems for the homogeneous and inhomogeneous fractional Helmholtz equation where fractional derivatives in the sense of Caputo and Riemann–Liouville are applied.
Nelson Vieira +3 more
wiley +1 more source
Optimal sampling and reduced modeling
, 2023 Cette thèse porte d’une part sur la conception de modèles réduits qui approchent optimalement des classes complexes de fonctions, et d’autre part sur l’utilisation de ces modèles réduits pour reconstruire des fonctions à partir d’un nombre limité de ...
Dolbeault, Matthieu
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Multidomain spectral approach to rational‐order fractional derivatives
Studies in Applied Mathematics, Volume 152, Issue 4, Page 1110-1132, May 2024.Abstract We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a multidomain approach; after transformations in accordance with the underlying Zq$Z_{q}$ curve ensuring ...
Christian Klein, Nikola Stoilov
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Échantillonnage optimal et réduction de modèle
, 2023 This thesis is concerned, on the one hand, with the design of reduced order models that optimally approximate complex classes of functions, and on the other hand with the use of such reduced models to recover functions from a limited amount of ...
Dolbeault, Matthieu
core