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Everything about Singular trace
Noncommutative geometric structure
In mathematics, a singular trace is a trace on a space of linear operators of a separable Hilbert space that vanishes on operators of finite rank. Singular traces are a feature of infinite-dimensional Hilbert spaces such as the space of square-summable sequences and spaces of square-integrable functions. Linear operators on a finite-dimensional Hilbert space have only the zero functional as a singular trace since all operators have finite rank. For example, matrix algebras have no non-trivial singular traces and the matrix trace is the unique trace up to scaling. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Singular traceA 5-minute orientation
- Skim a recent paper: The Wave Trace and Resonances of the Magnetic Hamiltonian with Singular Vector PotentialsInfluential work since 2022
- Pick up a classic book: Harmonic analysisThe most-reprinted book on the subject
- Read the landmark paper: Stable trace formula: Elliptic singular termsCited 155 times
- Go sideways: Commutator subspaceA closely related topic
- Go sideways: Weak trace-class operatorA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Stable trace formula: Elliptic singular terms
Interpolated multichannel singular spectrum analysis: A reconstruction method that honors true trace coordinates
Trace Formula for Sturm--Liouville Operators with Singular Potentials
ON THE DEFINITIONS OF SOBOLEV AND BV SPACES INTO SINGULAR SPACES AND THE TRACE PROBLEM
Trace formulae and singular values of resolvent power differences of self-adjoint elliptic operators
Trace Minimization of Singular Systems with Cross-Equation Restrictions
Asymptotic analysis of singular values of rectangular complex matrices in the Laguerre and fixed-trace ensembles
Trace Minimization of Singular Systems with Cross-Equation Restrictions
🆕 Influential since 2022
The Wave Trace and Resonances of the Magnetic Hamiltonian with Singular Vector Potentials
Singular Trace of 3D-Vector Fields and the Corresponding Boundary Value Problems
The singular value function, associated with a Maharam trace
Double-variable trace maximization for extreme generalized singular quartets of a matrix pair: A geometric method
Trace of the Monodromy Matrix of an Irregular Singular Point of a Linear System of First-Order Ordinary Differential Equations
📚 Books worth reading
- 📕Harmonic analysisBarry Simon · 2015
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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