Helffer–Sjöstrand formula
Appearance
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In mathematics, more specifically, in functional analysis, the Helffer-Sjöstrand formula is a formula for computing a function of a self-adjoint operator.
Background
[edit]If , then we can find a function such that , and for each , there exists a such that
Such a function is called an almost analytic extension of .[1]
The Formula
[edit]If and is a self-adjoint operator on a Hilbert space, then
where is an almost analytic extension of , and .
See also
[edit]References
[edit]- ^ Dimassi, M., & Sjöstrand, J. (1999). Spectral Asymptotics in the Semi-Classical Limit. London Mathematical Society Lecture Note Series (268). Cambridge University Press. Chapter 8. ISBN 9780511662195.
- ^ Hörmander, L. (1983). The Analysis of Linear Partial Differential Operators I. Distribution Theory and Fourier Analysis. Springer Verlag. Theorem 3.1.11. ISBN 9783540123274.