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Domain Perturbations, Shift of Eigenvalues and Capacity

✍ Scribed by André Noll

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
209 KB
Volume
170
Category
Article
ISSN
0022-1236

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✦ Synopsis

The notion of capacity of a subspace which was introduced in [16] is used to prove new estimates on the shift of the eigenvalues which arises if the form domain of a self-adjoint and semibounded operator is restricted to a smaller subspace. The upper bound on the shift of the spectral bound given in [16] is improved and another lower bound is proved which leads to a generalization of Thirring's inequality if the underlying Hilbert space is an L 2 -space. Moreover we prove a similar capacitary upper bound for the second eigenvalue. The results are applied to elliptic constant coefficient differential operators of arbitrary order. Finally it is given a capacitary characterization for the shift of the spectral bound being positive which works for operators with spectral bound of arbitrary type.

📜 SIMILAR VOLUMES

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