Sobolev theory for non commutative tori

zbMath0757.46061MaRDI QIDQ1192078

Mauro Spera

Publication date: 27 September 1992

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=RSMUP_1991__86__143_0

zbMATH Keywords

embeddingLaplacianSobolev normsHilbert-Schmidt normuniversal \(C^*\)-algebraskew symmetric bilinear form\(H^ s\)-topological moduleextension of Sobolev theory to non commutative algebrasnormalized finite faithful trace

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87)

Related Items (13)

Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori ⋮ Harmonic analysis on quantum tori ⋮ Laplace-Beltrami operators on noncommutative tori ⋮ A noncommutative Tauberian theorem and Weyl asymptotics in noncommutative geometry ⋮ A \(C^*\)-algebraic approach to the principal symbol. II ⋮ Functional calculus for elliptic operators on noncommutative tori. I ⋮ Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori ⋮ Quantum differentiability on noncommutative Euclidean spaces ⋮ Quantum differentiability on quantum tori ⋮ Function spaces on quantum tori ⋮ Pseudodifferential calculus on noncommutative tori, II. Main properties ⋮ Dixmier trace formulas and negative eigenvalues of Schrödinger operators on curved noncommutative tori ⋮ Sharp estimates of noncommutative Bochner-Riesz means on two-dimensional quantum tori

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