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Showing 1 to 9 of 9 for “"Toeplitz operators"”.
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Toeplitz operators
Thesis: M.S., Massachusetts Institute of Technology, Department of Mathematics, 1977
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Algebras of Toeplitz Operators
In this work we examine C*-algebras of Toeplitz operators over the unit ball in ℂ<sup>n</sup> and the unit polydisc in ℂ². Toeplitz operators are interesting examples of non-normal operators that generate non-commutative C*-algebras. Moreover, in the nice cases (depending on the geometry of the …
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Properties of truncated Toeplitz operators
We discuss the multiplication of truncated Toeplitz operators: or TTOs) on backward shift invariant subspaces of the Hardy space of the unit disc. Specifically we discuss when the product of two TTOs is itself a TTO, finding an equivalent to a similar result of Brown and Halmos for ordinary …
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Exploring the Numerical Range of Block Toeplitz Operators
… will explore the numerical range of the block Toeplitz operator with symbol function \(\phi(z)=A_0+zA_1\), where \(A_0, A_1 \in M_2(\mathbb{C})\). A full characterization of the numerical range of this operator proves to be quite difficult and so we will focus on characterizing the boundary of …
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Block Toeplitz operators with rational symbols and discrete singular systems
This thesis concerns block Toeplitz operators (equations). Consider the block Toeplitz operator T = [<I> k-j ]k,j=O' where the <I>k are complex m x m matrices such that 00 (0.1) v=-oo The norm in (0.1) is the usual operator norm on an m x m matrix. The condition (0.1) means that the symbol 00 ( …
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An Embedded Toeplitz Problem
In this work we investigate multi-variable Toeplitz operators and their relationship with KK-theory in order to apply this relationship to define and analyze embedded Toeplitz problems. In particular, we study the embedded Toeplitz problem of the unit disk into the unit ball in C^2. The embedding …
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Random partitions and the quantum Benjamin-Ono hierarchy
… Nazarov-Sklyanin (2013). L is expressed through Toeplitz operators whose symbols are affine Kac-Moody currents for gl1. We use the spectral shift function of L to construct a generating function y(u) of local Hamiltonians commuting with y3. This explicit y(u) is a special case of the y-operator …
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Toeplitzness of Composition Operators and Parametric Toeplitzness
… <span>\mathbb{U}</span>-automorphic composition operators, acting on the monomial basis for $H^2(\mathbb{U})$; which is used as one of the major tools later in Chapter 3.</p><p>In Chapter 2, we introduce the class of Parametric Toepliz operators(PTOs) as the solutions to the …