Temat: subordinacy theory - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Weyl-Titchmarsh type formula for Hermite operator with small perturbation
Autorzy:: Simonov, S.
Powiązania:: https://bibliotekanauki.pl/articles/255278.pdf
Data publikacji:: 2009
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Jacobi matrices
absolutely continuous spectrum
subordinacy theory
Weyl-Titchmarsh theory
Opis:: Small perturbations of the Jacobi matrix with weights √n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is an analogue of the classical Weyl-Titchmarsh formula for the Schr ödinger operator on the half-line with summable potential. Additionally, a base of generalized eigenvectors for "free" Hermite operator is studied and asymptotics of Plancherel-Rotach type are obtained.
Źródło:: Opuscula Mathematica; 2009, 29, 2; 187-207
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A first-order spectral phase transition in a class of periodically modulated Hermitian Jacobi matrices
Autorzy:: Pchelintseva, I.
Powiązania:: https://bibliotekanauki.pl/articles/255740.pdf
Data publikacji:: 2008
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Jacobi matrices
spectral phase transition
absolutely continuous spectrum
pure point spectrum
discrete spectrum
subordinacy theory
asymptotics of generalized eigenvectors
Opis:: We consider self-adjoint unbounded Jacobi matrices with diagonal q(n) = b(n)n and off-diagonal entries λ(n) = n, where b(n) is a 2-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum of the operator is either purely absolutely continuous or discrete. We study the situation where the spectral phase transition occurs, namely the case of b(1)b(2) = 4. The main motive of the paper is the investigation of asymptotics of generalized eigenvectors of the Jacobi matrix. The pure point part of the spectrum is analyzed in detail.
Źródło:: Opuscula Mathematica; 2008, 28, 2; 137-150
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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