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

For a real non-signdefinite function B(z), z ∈C, 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 ΔF = B. The answer is known for the function B with co...

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Autores principales:	Rozenblum,Grigori, Shirokov,Nikolay
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2010
Materias:	Pauli operators Zero modes Entire functions
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100011
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spelling	oai:scielo:S0719-064620100001000112018-10-08Entire Functions in Weighted L2 and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic FieldRozenblum,GrigoriShirokov,Nikolay Pauli operators Zero modes Entire functions For a real non-signdefinite function B(z), z ∈C, 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 ΔF = 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.12 n.1 20102010-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100011en10.4067/S0719-06462010000100011
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Pauli operators Zero modes Entire functions
spellingShingle	Pauli operators Zero modes Entire functions Rozenblum,Grigori Shirokov,Nikolay Entire Functions in Weighted L2 and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field
description	For a real non-signdefinite function B(z), z ∈C, 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 ΔF = 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.
author	Rozenblum,Grigori Shirokov,Nikolay
author_facet	Rozenblum,Grigori Shirokov,Nikolay
author_sort	Rozenblum,Grigori
title	Entire Functions in Weighted L2 and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field
title_short	Entire Functions in Weighted L2 and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field
title_full	Entire Functions in Weighted L2 and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field
title_fullStr	Entire Functions in Weighted L2 and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field
title_full_unstemmed	Entire Functions in Weighted L2 and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field
title_sort	entire functions in weighted l2 and zero modes of the pauli operator with non-signdefinite magnetic field
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2010
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100011
work_keys_str_mv	AT rozenblumgrigori entirefunctionsinweightedl2andzeromodesofthepaulioperatorwithnonsigndefinitemagneticfield AT shirokovnikolay entirefunctionsinweightedl2andzeromodesofthepaulioperatorwithnonsigndefinitemagneticfield
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Entire Functions in Weighted L2 and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field

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