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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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      Abstract

      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.

      Translated abstract

      Para una función no signo definida B(z), z ∈ C, investigamos la dimensión del espacio de funciones analíticas enteras de cuadrado integrable con peso e ±2F , donde la función F(z) = F(x1, x2) verifica la ecuación de Poisson ΔF = B. La respuesta es conocida para la función B con signo constante. Discutimos algunas clases de funciones B no signo definida e positivamente homogéneas, donde dimensión zero y infinita pueden ocurrir. En el caso anterior nosotros presentamos un método de construir funciones enteras con un comportamiento en infinito prescrito en diferentes direcciones. El tópico es estrechamente relacionado con la cuestión de la dimensión del subespacio de energía zero para el operador de Pauli.

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      Most cited references 5

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      Spectral properties of Schrödinger operators with magnetic fields for a spin 12 particle

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        An Introduction to Complex Analysis in Several Variables

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          Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields

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            Author and article information

            Affiliations
            [1 ] University of Gothenburg Sweden
            [2 ] St. Petersburg State University Russia
            Contributors
            Role: ND
            Role: ND
            Journal
            cubo
            Cubo (Temuco)
            Cubo
            Universidad de La Frontera. Departamento de Matemática y Estadística (Temuco )
            0719-0646
            2010
            : 12
            : 1
            : 115-132
            S0719-06462010000100011
            10.4067/S0719-06462010000100011

            http://creativecommons.org/licenses/by/4.0/

            Product
            Product Information: SciELO Chile
            Categories
            MATHEMATICS
            MATHEMATICS, APPLIED

            Applied mathematics, General mathematics

            Entire functions, Zero modes, Pauli operators

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