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Results tagged with ca.classical-analysis-and-odes
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user 3709
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
12
votes
1
answer
1k
views
Path integrals, localisation
Physicists use the "Atiyah-Bott formula" for path "integrals" (for instance the supersymmetric proof of the Atiyah-Singer index theorem. Is there some way to make atleast some of these ideas rigorous? …
- 3,383
3
votes
1
answer
461
views
Regarding Discrete Eigenvalues
For many eigenvalue problems for differential operators (for example the quantum harmonic oscillator (HO)), unless we impose some behaviour at infinity, the eigenvalues will not be discrete.
But, supp …
- 3,383
1
vote
1
answer
309
views
References for weak ellipticity
There are good books (like Evans) for strongly elliptic second order linear PDE. I want to learn about weakly elliptic PDE (of any order). Are there any good books for the same? I am very curious as t …
- 3,383
1
vote
2
answers
1k
views
Lipschitz continuity of eigenvalues and eigenvectors of Hermitian matrices
It is well-known that the eigenvalues (in decreasing order) of a Hermitian matrix $A$ are Lipschitz continuous functions of $A$.
Do there exist orthonormal eigenvectors that vary in a Lipschitz contin …
- 3,383