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Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.

3 votes
0 answers
79 views

Boundedness for resolvents of perturbed operators

( might not be a research-level question... if it violates any term of this website I will delete it ASAP ) I'm wondering if there is any way to show the boundedness/unboundedness of operators like $ …
alby's user avatar
  • 91
2 votes
0 answers
44 views

Potential scattering for non-decaying potential

I am reading this note on potential scattering by Siu-Hung Tang and Maciej Zworski. Just wondering if there is a scattering theory for the Schrödinger with a non-decaying potential $- \Delta + V$ on t …
alby's user avatar
  • 91
1 vote
1 answer
171 views

Lower bound of the spectrum of a Schrodinger operator on a bounded domain

I am trying to look for references on estimate of the lower bound of the spectrum of a Schrodinger operator $-\Delta + V$ on a bounded domain in three-dimensional space. For simplicity, we can take th …
alby's user avatar
  • 91