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Full-Text Articles in Mathematics
Unitary Equivalence To A Truncated Toeplitz Operator: Analytic Symbols, Stephan Ramon Garcia, Daniel E. Poore '11, William T. Ross
Unitary Equivalence To A Truncated Toeplitz Operator: Analytic Symbols, Stephan Ramon Garcia, Daniel E. Poore '11, William T. Ross
Pomona Faculty Publications and Research
Unlike Toeplitz operators on H², truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this paper we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive, and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension ≤ 3 is unitarily equivalent to a direct sum of truncated Toeplitz operators.
The Norm Of A Truncated Toeplitz Operator, Stephan Ramon Garcia, William T. Ross
The Norm Of A Truncated Toeplitz Operator, Stephan Ramon Garcia, William T. Ross
Pomona Faculty Publications and Research
We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the H2 and H∞ norms of functions in model spaces.
Interpolation And Complex Symmetry, Stephan Ramon Garcia, Mihai Putinar
Interpolation And Complex Symmetry, Stephan Ramon Garcia, Mihai Putinar
Pomona Faculty Publications and Research
In a separable complex Hilbert space endowed with an isometric conjugate-linear involution, we study sequences orthonormal with respect to an associated bilinear form. Properties of such sequences are measured by a positive, possibly unbounded angle operator which is formally orthogonal as a matrix. Although developed in an abstract setting, this framework is relevant to a variety of eigenvector interpolation problems arising in function theory and in the study of differential operators.
Conjugation And Clark Operators, Stephan Ramon Garcia
Conjugation And Clark Operators, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.