Entire Functions in Weighted 𝘓₂ and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field

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DOI:

https://doi.org/10.4067/S0719-06462010000100011

Abstract

For a real non-signdefinite function B(z), z ∈ â„‚, we investigate the dimension of the space of entire analytical functions square integrable with weight e±2F, where the function F(z) = F(x1, x2) satisfies the Poisson equation ∆F = B. The answer is known for the function B with constant sign. We discuss some classes of non-signdefinite positively homogeneous functions B, where both infinite and zero dimension may occur. In the former case we present a method of constructing entire functions with prescribed behavior at infinity in different directions. The topic is closely related with the question of the dimension of the zero energy subspace (zero modes) for the Pauli operator.

Keywords

Pauli operators , Zero modes , Entire functions
  • Grigori Rozenblum Department of Mathematics, Chalmers University of Technology, and Department of Mathematics University of Gothenburg, S-412 96 Gothenburg, Sweden.
  • Nikolay Shirokov Department of Mathematics and Mechanics, St. Petersburg State University, Russia.
  • Pages: 115–132
  • Date Published: 2010-03-01
  • Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal

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Published

2010-03-01

How to Cite

[1]
G. Rozenblum and N. Shirokov, “Entire Functions in Weighted 𝘓₂ and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field”, CUBO, vol. 12, no. 1, pp. 115–132, Mar. 2010.

Issue

Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal

Section

Articles