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8 votes
1 answer
359 views

Lax pairs in an abstract formalism

I am reading Integrals of Nonlinear Equations of Evolution and Solitary Waves by Peter Lax and I'm having a hard time. The methods are pioneering, of course, but Lax does not bother much to provide ...
Delio Mugnolo's user avatar
7 votes
1 answer
938 views

What is the idea behind interpolation spaces?

I am working through a text on Numerics for SPDEs and there the concept an interpolation (Hilbert-)space associated to an operator is used. To be specific: Definition. Let $H$ be an $\mathbb{R}$-...
alexlo's user avatar
  • 131
1 vote
0 answers
33 views

Limiting absorption principle for higher powers of resolvents

Let $H$, $A$ be self-adjoint operators on a Hilbert space. Moreover, let $I$ be a bounded open interval contained in the spectrum of $H$. Assume that $H$,$A$ satisfy the following positive commutator ...
Janik's user avatar
  • 141