On polynomials in two projections.
Nonlinear transmission problems.
Analytic roots of invertible matrix functions.
Multiblock problems for almost periodic matrix functions of several variables.
Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem.
We define spectral factorization in L (or a generalized Wiener-Hopf factorization) of a measurable singular matrix function on a simple closed rectifiable contour Γ. Such factorization has the same uniqueness properties as in the nonsingular case. We discuss basic properties of the vector valued Riemann problem whose coefficient takes singular values almost everywhere on Γ. In particular, we introduce defect numbers for this problem which agree with the usual defect numbers in the case of a nonsingular...
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.
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