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Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis

James Adduci, Boris Mityagin (2012)

Open Mathematics

For any complex valued L p-function b(x), 2 ≤ p < ∞, or L ∞-function with the norm ‖b↾L ∞‖ < 1, the spectrum of a perturbed harmonic oscillator operator L = −d 2/dx 2 + x 2 + b(x) in L 2(ℝ1) is discrete and eventually simple. Its SEAF (system of eigen- and associated functions) is an unconditional basis in L 2(ℝ).

Eighty fifth anniversary of birthday and scientific legacy of Professor Miloš Ráb

Ondřej Došlý, Eva Jansová, Josef Kalas (2014)

Archivum Mathematicum

The paper is concentrated on Professor Miloš Ráb and his contribution to the theory of oscillatory properties of solutions of second and third order linear differential equations, the theory of differential equations with complex coefficients and dynamical systems, and the theory of nonlinear second order differential equations. At the beginning, we take a brief look at the most important moments in his life. Afterwards, we describe his scientific activities on mentioned theories.

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