Zobrazeno 1 - 10
of 221
pro vyhledávání: '"Yafaev, D."'
Autor:
Yafaev, D. R.
Spectral properties of Jacobi operators $J$ are intimately related to an asymptotic behavior of the corresponding orthogonal polynomials $P_{n}(z)$ as $n\to\infty$. We study the case where the off-diagonal coefficients $a_{n}$ and, eventually, diagon
Externí odkaz:
http://arxiv.org/abs/2305.19680
Autor:
Yafaev, D. R.
We find and discuss asymptotic formulas for orthonormal polynomials $P_{n}(z)$ with recurrence coefficients $a_{n}, b_{n}$. Our main goal is to consider the case where off-diagonal elements $a_{n}\to\infty$ as $n\to\infty$. Formulas obtained are esse
Externí odkaz:
http://arxiv.org/abs/2202.02087
Autor:
Yafaev, D. R.
We consider second order differential equations with real coefficients that are in the limit circle case at infinity. Using the semiclassical Ansatz, we construct solutions (the Jost solutions) of such equations with a prescribed asymptotic behavior
Externí odkaz:
http://arxiv.org/abs/2106.04196
Autor:
Yafaev, D. R.
We consider symmetric Jacobi operators with recurrence coefficients such that the corresponding difference equation is in the limit circle case. Equivalently, this means that the associated moment problem is indeterminate. Our main goal is to find a
Externí odkaz:
http://arxiv.org/abs/2104.13609
Autor:
Yafaev, D. R.
Orthogonal polynomials $P_{n}(\lambda)$ are oscillating functions of $n$ as $n\to\infty$ for $\lambda$ in the absolutely continuous spectrum of the corresponding Jacobi operator $J$. We show that, irrespective of any specific assumptions on coefficie
Externí odkaz:
http://arxiv.org/abs/2011.14987
Autor:
Yafaev, D. R.
We study Jacobi operators $J_{p}$, $p> -1$, whose eigenfunctions are Laguerre polynomials. All operators $J_{p}$ have absolutely continuous simple spectra coinciding with the positive half-axis. This fact, however, by no means imply that the wave ope
Externí odkaz:
http://arxiv.org/abs/2007.08418
Autor:
Yafaev, D. R.
Our goal is to find an asymptotic behavior as $n\to\infty$ of the orthogonal polynomials $P_{n}(z)$ defined by Jacobi recurrence coefficients $a_{n}$ (off-diagonal terms) and $ b_{n}$ (diagonal terms). We consider the case $a_{n}\to\infty$, $b_{n}\to
Externí odkaz:
http://arxiv.org/abs/2006.02907
Autor:
Yafaev, D. R.
Our goal is to find asymptotic formulas for orthonormal polynomials $P_{n}(z)$ with the recurrence coefficients slowly stabilizing as $n\to\infty$. To that end, we develop spectral theory of Jacobi operators with long-range coefficients and study the
Externí odkaz:
http://arxiv.org/abs/1811.09254
Autor:
Yafaev, D. R.
Our goal is to develop spectral and scattering theories for the one-dimensional Schr\"odinger operator with a long-range potential $q(x)$, $x\geq 0$. Traditionally, this problem is studied with a help of the Green-Liouville approximation. This requir
Externí odkaz:
http://arxiv.org/abs/1810.03112