Random-weighted Sobolev inequalities on \(\mathbb{R}^d\) and application to Hermite functions

DOI10.1007/s00023-014-0317-5zbMath1310.81060arXiv1307.4976OpenAlexW2086276479MaRDI QIDQ2256023

Laurent Thomann, Aurélien Poiret, Didier Robert

Publication date: 19 February 2015

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.4976

zbMATH Keywords

Hermite functionsSobolev inequalitiesrandomization method

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Sobolev (and similar kinds of) spaces of functions of discrete variables (46E39)

Related Items (7)

Concentration and universal randomisation of proper subspaces ⋮ Scaling of harmonic oscillator eigenfunctions and their nodal sets around the caustic ⋮ On random Hermite series ⋮ Asymptotic Behavior of the Nonlinear Schrödinger Equation with Harmonic Trapping ⋮ Multidimensional Paley-Zygmund theorems and sharp \(L^p\) estimates for some elliptic operators ⋮ Random weighted Sobolev inequalities and application to quantum ergodicity ⋮ Expected values of eigenfunction periods

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