We obtain a representation formula for the trigonometric sum f (m, n) and deduce from it the upper bound f(m, n) < (4/p 2 ) m log m+ (4/p 2 )(c -log(p/2)+2C G ) m+O(m/`log m), where C G is the supremum of the function G(t) :=; . k=1 log |2 sin pkt|/(4k 2 -1), over the set of irrationals. The coeffi
Asymptotic Formulas for Determinants of a Sum of Finite Toeplitz and Hankel Matrices
โ Scribed by Estelle L. Basor; Torsten Ehrhardt
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 433 KB
- Volume
- 228
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In this paper we derive second-order asymptotic results for matrices Matrices of the above form can be thought of as variable-coefficient Toeplitz matrices, or a discrete analogue of a pseudodifferential operator. Ideas from pseudodifferential operator theory are used in the proof.
## Abstract Let __ฮป__ be an eigenvalue of an infinite Toeplitz band matrix __A__ and let __ฮป~n~__ be an eigenvalue of the __n__ ร__n__ truncation __A~n~__ of __A__ . Suppose __ฮป~n~__ converges to __ฮป__ as __n__ โ โ. We show that generically the eigenspaces for __ฮป~n~__ are onedimensional and contai
It is shown that certain sequences of Hankel matrices of finite rank obtained from a given sequence of complex numbers and powers of companion matrices are closely related. This relation is established by investigating the algebraic properties of combinations of polynomial multiples of powers of com
## Abstract We determine bounds for the spectral and ๐~__p__~ norm of CauchyโHankel matrices of the form __H__~__n__~=[1/(__g__+__h__(__i__+__j__))]^__n__^~__i,j__=1~โก ([1/(__g__+__kh__)]^__n__^~__i,j__=1~), __k__=0, 1,โฆ, __n__ โ1, where __k__ is defined by __i__+__j__=__k__ (mod __n__). Copyright