Spectral integration and spectral theory for non-Archimedean Banach spaces

Math 206: Banach Algebra and Spectral Theory

Spectral Theory of Linear Operators—and Spectral Systems in Banach Algebras, By

Let A be a bounded operator on a Banach space X. A scalar λ is in the spectrum of A if the operator A − λ is not invertible. Case closed. What more is there to say? As anyone with the slightest exposure to operator theory will testify, there is so much out there that no book could come close to being comprehensive. What authors do in such situations is choose a small area or topic of interest t...

Non–Autonomous Non–Local Dispersal - Spectral Theory

In applications to spatial structure in biology and to the theory of phase transition, it has proved useful to generalize the idea of diffusion to a non-local dispersal with an integral operator replacing the Laplacian. We study the spectral problem for the linear scalar equation ut(x, t) = ∫ Ω K(x, y)u(y, t)dy+ h(x, t)u(x, t), and tackle the extra technical difficulties arising because of the ...

Descent for Non-archimedean Analytic Spaces

In the theory of schemes, faithfully flat descent is a very powerful tool. One wants a descent theory not only for quasi-coherent sheaves and morphisms of schemes (which is rather elementary), but also for geometric objects and properties of morphisms between them. In rigid-analytic geometry, descent theory for coherent sheaves was worked out by Bosch and Görtz [BG, 3.1] under some quasi-compac...

Tropical varieties for non-archimedean analytic spaces

For the whole paper, K denotes an algebraically closed field endowed with a nontrivial non-archimedean complete absolute value | |. The corresponding valuation is v := − log | | with value group Γ := v(K). The valuation ring is denoted by K. Note that the residue field K̃ is algebraically closed. In Theorem 1.3, §8 and in the second part of §9, we start with a field K endowed with a discrete val...