Sobolev spaces associated to the harmonic oscillator

2006/08/28 by Bruno Bongioanni, Bongioanni, B, J. L. Torrea +1 · 4 citations
Computer Science · Mathematics · #42B35 #42C05 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.math/0608684

openalex publication_date 2006/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the Hermite--Sobolev spaces naturally associated to the harmonic oscillator H= -Δ+|x|². Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.

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