Bo Wu: Negative spectrum of Schrodinger operators with fractal potentials and pseudo-differential equations on local fields

Föreläsare/Lecturer

Bo Wu

Titel/Title

Negative spectrum of Schrodinger operators with fractal potentials and pseudo-differential equations on local fields

Sammanfattning/Abstract

The study focuses on the fractal PDE from both macroscopic and microscopic aspect, namely over the Euclidean space and the local fields. From macroscopic view point, this study investigates the negative spectrum of Schrodinger operators with fractal potentials, using fractal pseudo-differential operators on the basis of the theory of function space which created by Has Triebel. The main idea is to improve the Triebel B-type space which the operator act in. We obtain anisotropic B-type space from defining anisotropy number, anisotropy distance function. On the other hand, we change the iteration mechanism of nonisotropic fractal setting to make the fractal sets more regular. And then we use the decomposition technique to arrive the sharp estimate of the negative spectrum of Schrodinger operators. Thereby we improved Has Triebel's work. From microscopic view point, we found the exact solutions for some pseudo-differential equations over p-adic fields applying p-adic derivative and the orthonormal basis established by Su Weiyi and Qiu Hua. The main idea is to use the methodology of separation of variables, making the proposed pseudo-differential equations reduced to ODE.

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