Extreme eigenvalues of toeplitz operators
نویسندگان
چکیده
منابع مشابه
On the Extreme Eigenvalues of Toeplitz Matrices
The matrix Tn[/] = (C„_y), 5, 7 = 0, 1, •• -, re is called the wth finite section of the infinite Toeplitz matrix (C,-¡) associated with the function f(9). We will be concerned with functions f(6) satisfying Condition A. Let f(d) be real, continuous and periodic with period 2w. Let min f(B) =/(0) = 0 and let 6 = 0 be the only value of 0 (mod 2tt) for which this minimum is attained. Condition A(...
متن کاملRemarks on Extreme Eigenvalues of Toeplitz Matrices
Let f be a nonnegative integrable function on [-r,r], T.Cf) the Ca+l) X(n+l) Toeplitz matrix associated with f and k,. its smallest eigenvalue. It is shown that the convergence of )t,. to rain f(O) can be exrmnentiallv fast even when f does not satisfy the smoothness condition of Kae, Murdoeh and Szeg6 (1953). Also a lower bound for ),,. corresponding to a large class of functions which do not ...
متن کاملExtreme eigenvalues of real symmetric Toeplitz matrices
We exploit the even and odd spectrum of real symmetric Toeplitz matrices for the computation of their extreme eigenvalues, which are obtained as the solutions of spectral, or secular, equations. We also present a concise convergence analysis for a method to solve these spectral equations, along with an efficient stopping rule, an error analysis, and extensive numerical results.
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We derive upper and lower bounds on the smallest and largest eigenvalues, respectively, of real symmetric Toeplitz matrices. The bounds are rst obtained for positive-deenite matrices and then extended to the general real symmetric case. Our bounds are computed as the roots of rational and polynomial approximations to spectral, or secular, equations. The decomposition of the spectrum into even a...
متن کاملThe eigenvalues of limits of radial Toeplitz operators
Let A2 be the Bergman space on the unit disk. A bounded operator S on A2 is called radial if Szn = λnz n for all n ≥ 0, where λn is a bounded sequence of complex numbers. We characterize the eigenvalues of radial operators that can be approximated by Toeplitz operators with bounded symbols.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1983
ISSN: 0001-8708
DOI: 10.1016/0001-8708(83)90077-4