×

zbMATH — the first resource for mathematics

Semigroup domination and eigenvalue estimates. (English. Russian original) Zbl 1015.47023
St. Petersbg. Math. J. 12, No. 5, 831-845 (2001); translation from Algebra Anal. 12, No. 5, 158-177 (2001).
Using the domination \(|e^{-tS}|\leq e^{-tT}\), \(t \geq 0 \), between two selfadjoint semigroups \((e^{-tS})_{t\geq 0} \) and \((e^{-tT})_{t\geq 0 }\) on \( L^2\)-spaces, the author obtains eigenvalue estimates for \(S\) from the ones for \(T\). Applications to magnetic Schrödinger operators are given.

MSC:
47D06 One-parameter semigroups and linear evolution equations
35P15 Estimates of eigenvalues in context of PDEs
47A10 Spectrum, resolvent
47B38 Linear operators on function spaces (general)
47B65 Positive linear operators and order-bounded operators
PDF BibTeX XML Cite