Let £f be a complex number in the closed unit disk D , And H be a separable Hilbert space with the orthonormal basis , say ,£`= {e_n:n=0,1,2,¡K}. A bounded operator T on H is called a £f- Toeplitz operator if <Te_(n+1) ,e_(m+1) >=£f<Te_n ,e_m > (where < , > is inner product on H) The L^2 function £p~ £Ua_n e^in£c with a_n=<Te_0 ,e_n> for n>=0 , and a_n=<Te_n ,e_0 > for n<0 is , on the other hand , called the symbol of T The subject arises naturally from a special case of the operator equation S^* AS=£fA+B where S is a shift on H , which plays an essential role in finding bounded matrix (a_ij ) on L^2 (Z) that solves the system of equations {((a_(2i,2j) =p_ij+aa_ij@a_(2i,2j-1) =q_ij+ba_ij )@a_(2i-1,2j) =£h_ij+ca_ij@a_(2i-1,2j-1) =£s_ij+da_ij ) ¢t, for all i ,j belong Z , where (p_ij ) ,(q_ij ) ,(£h_ij ) ,(£s_ij ) are bounded matrices on l^2 (Z) and a ,b ,c ,d belong C . It is also clear that the well-known Toeplitz operators are precisely the solutions of S^* AS=A , when S is the unilateral shift . In this paper , we will determine the spectra of £f- Toeplitz operators with |£f|=1 of finite order, and when the symbols are analytic with C^1 boundary values.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 110-116). Also available via the Internet.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Master of Science. Johannesburg, March 2015. / The primary purpose of this study is to investigate the asymptotic distribution of the eigenvalues of self-adjoint second order di erential operators. We rst analyse the problem where the functions g and h are equal to zero. To improve on the terms of the eigenvalue problem for g; h = 0, we consider the eigenvalue problem for general functions g and h. Here we calculate explicitly the rst four terms of the eigenvalue asymptotics problem.

by Lai May-lun. / Thesis (M.B.A.)--Chinese University lof Hong Kong, 1981. / Bibliography: leaves 61-63.

After our introduction in Chapter 1, we consider van der Corput's lemma in Chapter 2. We find the nodes that minimize divided differences, and use these to find the sharp constant in a related sublevel set estimate. We go on to find the sharp constant in the first instance of the van der Corput lemma using a complex mean value theorem for integrals. With these bounds we improve the constant in the general van der Corput lemma, so that it is asymptotically sharp. In Chapter 3 we review the p-adic numbers and some results from Fourier analysis over the p-adics. In Chapter 4 we prove a p-adic version of van der Corput's lemma for polynomials, opening the way for the study of oscillatory integrals over the p-adics. In Chapter 5 we apply this result to bound maximal averages. We show that maximal averages over curves defined by p-adic polynomials are Lq bounded, where 1&ltq&ltinfinity

Thesis (Ph. D.)--Oregon State University, 1983. / Typescript (photocopy). Includes bibliographical references (leaves 71-74). Also available on the World Wide Web.

In this dissertation we study certain classes of operators on a separable, complex, in??nite dimensional Hilbert space H, speci??cally from the point of view of properties of the hyperlattice (i.e., lattice of hyperinvariant subspaces) for such operators. We show that every (BCP)-operator in C00 is hyperquasisimilar to a quasidiagonal (BCP)- operator in C00. Moreover we show that there exists a ??xed block diagonal (BCP)- operator Bu with the property that if every compact perturbation Bu + K of Bu in (BCP) and C00 with kKk < " has a nontrivial hyperinvariant subspace, then every nonscalar operator on H has a nontrivial hyperinvariant subspace. This shows that the study of the structure of the hyperlattice of an arbitrary operator on Hilbert space is essentially equivalent to the study of the hyperlattice structure of some much smaller, special classes of operators, and it is these on which we concentrate. Moreover, we study some special subclasses (B??) and (S??) of the class of in- vertible (BCP)-operators with a view of obtaining some insight into the problem of determining the structure of operators in these classes.

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

Thesis--Delft. / Stellingen: 4 p. inserted. Summary in Dutch. Includes bibliographical references.