Eigenvalues of singular measures and Connes' noncommutative integration
From MaRDI portal
Publication:2120169
DOI10.4171/JST/401zbMath1486.35316arXiv2103.02067OpenAlexW3134427992MaRDI QIDQ2120169
Publication date: 31 March 2022
Published in: Journal of Spectral Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.02067
Pseudodifferential operators as generalizations of partial differential operators (35S05) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Noncommutative global analysis, noncommutative residues (58J42) Pseudodifferential operators (47G30)
Related Items
Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori, Weyl's laws and Connes' integration formulas for matrix-valued \(L\!\log \!L\)-Orlicz potentials, A noncommutative Tauberian theorem and Weyl asymptotics in noncommutative geometry, Connes integration formula: a constructive approach, Connes' integration and Weyl's laws, Spectral estimates and asymptotics for integral operators on singular sets, Lieb-Thirring estimates for singular measures, Eigenvalues of the Birman-Schwinger operator for singular measures: the noncritical case, Dixmier trace formulas and negative eigenvalues of Schrödinger operators on curved noncommutative tori
Cites Work
- Dixmier traces and non-commutative analysis
- Potential type operators and transmission problems for strongly elliptic second-order systems in Lipschitz domains
- An equivariant noncommutative residue
- Measure theory in noncommutative spaces
- Geometry of measures in \(R^ n:\) Distribution, rectifiability, and densities
- A last theorem of Kalton and finiteness of Connes' integral
- Eigenvalue asymptotics for potential type operators on Lipschitz surfaces
- Banach limits and traces on \(\mathcal{L}_{1, \infty}\)
- Partial differential equations. II: Qualitative studies of linear equations
- Measures from Dixmier traces and zeta functions
- The action functional in non-commutative geometry
- Piecewise-polynomial approximation of functions from \(H^ \ell((0,1)^ d)\), \(2\ell=d\), and applications to the spectral theory of the Schrödinger operator
- The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\)
- On Schrödinger operators perturbed by fractal potentials
- The eigenvalue behaviour for the boundary value problems related to self- similar measures on \(\mathbb{R}^ d\)
- Traces of compact operators and the noncommutative residue
- Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case
- Eigenvalue asymptotics for weighted polyharmonic operator with a singular measure in the critical case
- An estimate for the Morse index of a Stokes wave
- Assouad type dimensions and homogeneity of fractals
- The Negative Spectrum of Schrödinger Operators with Fractal Potentials
- On negative eigenvalues of two-dimensional Schrödinger operators with singular potentials
- Eigenvalue asymptotics for potential type operators on Lipschitz surfaces of codimension greater than 1
- The Landau Hamiltonian with δ-potentials supported on curves
- Geometry of Banach limits and their applications
- On negative eigenvalues of two‐dimensional Schrödinger operators
- Strong Coupling Asymptotics for a Singular Schrödinger Operator with an Interaction Supported by an Open Arc
- On negative eigenvalues of generalized Laplace operators.
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
