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Research paper thumbnail of Almost periodicity of some Jacobi matrices

Proceedings / Indian Academy of Sciences

Research paper thumbnail of Inverse spectral theory for Jacobi matrices and their almost periodicity

In this paper we consider the inverse problem for bounded Jacobi matrices with nonempty absolutel... more In this paper we consider the inverse problem for bounded Jacobi matrices with nonempty absolutely continuous spectrum and as an application show the almost periodicity of some random Jacobi matrices. We do the inversion in two different ways. In the general case we use a direct method of reconstructing the Green functions. In the special case where we show the almost periodicity, we use an alternative method using the trace formula for points in the orbit of the matrices under translations. This method of reconstruction involves analyzing the Abel-Jacobi map and solving of the Jacobi inversion problem associated with an infinite genus Riemann surface constructed from the spectrum. Contents 1 Introduction 2 1.1 Ideas, strategies and limitations : : : : : : : : : : : : : : : : : 4 2 Inverse Spectral Theory 8 3 Interpolation theorem 18 4 Analysis on a Riemann surface 32 4.1 The Riemann Surface : : : : : : : : : : : : : : : : : : : : : : : 32 4.2 The Abel-Jacobi map : : : : : : : : :...

Research paper thumbnail of Almost periodicity of some Jacobi matrices

Proceedings / Indian Academy of Sciences

Research paper thumbnail of Inverse spectral theory for Jacobi matrices and their almost periodicity

In this paper we consider the inverse problem for bounded Jacobi matrices with nonempty absolutel... more In this paper we consider the inverse problem for bounded Jacobi matrices with nonempty absolutely continuous spectrum and as an application show the almost periodicity of some random Jacobi matrices. We do the inversion in two different ways. In the general case we use a direct method of reconstructing the Green functions. In the special case where we show the almost periodicity, we use an alternative method using the trace formula for points in the orbit of the matrices under translations. This method of reconstruction involves analyzing the Abel-Jacobi map and solving of the Jacobi inversion problem associated with an infinite genus Riemann surface constructed from the spectrum. Contents 1 Introduction 2 1.1 Ideas, strategies and limitations : : : : : : : : : : : : : : : : : 4 2 Inverse Spectral Theory 8 3 Interpolation theorem 18 4 Analysis on a Riemann surface 32 4.1 The Riemann Surface : : : : : : : : : : : : : : : : : : : : : : : 32 4.2 The Abel-Jacobi map : : : : : : : : :...

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