Transient behavior of powers and exponentials of large Toeplitz matrices.
The algebraic Riccati equation with Toeplitz matrices as coefficients.
Schatten norms of Toeplitz matrices with Fisher--Hartwig singularities.
The norm of the product of a large matrix and a random vector.
Probability against condition number and sampling of multivariate trigonometric random polynomials.
Truncated Toeplitz Operators on the Polydisk.
On the singular values and eigenvalues of the Fox-Li and related operators.
Algebraic and essentially algebraic composition operators on C(X).
Spectral approximation for Segal-Bargmann space Toeplitz operators
Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk or on the Segal-Bargmann space over . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression of A to the linear span of the monomials . Unfortunately, in general the spectrum of does not mimic the spectrum of A as...
Wiener-Hopf integral operators with PC symbols on spaces with Muckenhoupt weight.
We describe the spectrum and the essential spectrum and give an index formula for Wiener-Hopf integral operators with piecewise continuous symbols on the space L(R,ω) with a Muckenhoupt weight ω. Our main result says that the essential spectrum is a set resulting from the essential range of the symbol by joining the two endpoints of each jump by a certain sickle-shaped domain, whose shape is completely determined by the value of p and the behavior of the weight ω at the origin and at infinity.
Algebras of Toeplitz operators with oscillating symbols.
This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form b[e] where b belongs to some algebra of functions on the unit circle and a is a fixed orientation-preserving homeomorphism of the real line onto itself. We prove the existence of certain interesting homomorphisms and establish conditions for the normal solvability, Fredholmness, and invertibility of operators in these algebras.
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