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Everything about Trace operator
Boundary condition for generalized functions
In mathematical analysis, the trace operator extends the notion of the restriction of a function to the boundary of its domain to "generalized" functions in a Sobolev space. This is particularly important for the study of partial differential equations with prescribed boundary conditions, where weak solutions may not be regular enough to satisfy the boundary conditions in the classical sense of functions. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Trace operatorA 5-minute orientation
- Skim a recent paper: When do triple operator integrals take value in the trace class?Influential work since 2022
- Pick up a classic book: Kuznetsov's trace formula and the Hecke eigenvalues of Maass formsThe most-reprinted book on the subject
- Read the landmark paper: Linear transformations which preserve trace and positive semidefiniteness of operatorsCited 1,330 times
- Go sideways: Gradient discretisation methodA closely related topic
- Go sideways: Elliptic boundary value problemA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Linear transformations which preserve trace and positive semidefiniteness of operators
A trace class operator inequality
Generalized Morrey spaces and trace operator
The trace in finite operator algebras
Trace formulas for the schroedinger operator
Reduced operator algebras of trace-preserving quantum automorphism groups
The Lifshitz–Krein trace formula and operator Lipschitz functions
Operator Ideals with a Trace
🆕 Influential since 2022
When do triple operator integrals take value in the trace class?
Eigenvalue Asymptotics and a Trace Formula for a Fourth-Order Differential Operator
Spectral asymptotics and a trace formula for a fourth-order differential operator corresponding to thin film equation
The Concept of a Trace and the Boundedness of the Trace Operator in Banach-Sobolev Function Spaces
Trace formulae for a conformable fractional diffusion operator
📚 Books worth reading
- 📕Kuznetsov's trace formula and the Hecke eigenvalues of Maass formsAndrew Knightly · 2013
Eigenvalues of the Laplacian for Hecke triangle groupsDennis A. Hejhal · 1992- 📕Traces of Hecke operatorsAndrew Knightly · 2006
- 📕The trace formula for Hecke operators over rank one latticesWerner Hoffmann · 1986
- 📕The Selberg Trace Formula for PSL(2,O K) for imaginary quadratic number fields K of arbitrary class numberPia Bauer-Price · 1991
Scattering operator, Eisenstein series, inner product formula, and "Maass-Selberg" relations for Kleinian groupsNikolaos Mandouvalos · 1989
Functional inequalitiesN. Ghoussoub · 2013
Spectral analysis, differential equations, and mathematical physicsFritz Gesztesy, H. Holden · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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