Titlebook: Singular Integral Operators, Factorization and Applications; International Worksh Albrecht Böttcher,Marinus A. Kaashoek,Frank-Olme S Confer

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Factorization of Singular Integral Operators with a Carleman Shift via Factorization of Matrix Func circle. The main goal is to obtain a special factorization of the operator with the help of a factorization of a related matrix function in a suitable algebra. This factorization allows us to characterize the kernel and the range of the operator under consideration, similarly to the case of singular integral operators without shift.

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Criterion for the Fredholmness of Singular Operators with Piecewise Continuous Coefficients in Geneed Hölder space ..(Γ, ρ) together with a formula for the index. The conditions were given in terms of Boyd-type indices of the space ..(Γ, ρ). In this paper we prove that those conditions are also necessary for a singular integral operator to be Fredholm.

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Operator Theory: Advances and Applicationshttp://image.papertrans.cn/s/image/867880.jpg

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https://doi.org/10.1007/978-3-0348-8007-7Complex analysis; Integral equation; Operator theory; convolution; partial differential equation; partial

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Covariant Symbolic Calculi on Real Symmetric Domains,We introduce the concept of “covariant symbolic calculus” on real and complex symmetric domains, prove a general product formula for the link transform (generalized Berezin transform) between two such calculi, and describe a basic example (Toeplitz calculus) in more detail.

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Factorization Theorem for the Transfer Function Associated with an Unbounded Non-Self-Adjoint 2 X 2We construct operators which factorize the transfer function associated with a non-self-adjoint 2 x 2 operator matrix whose diagonal entries can have overlapping spectra and whose off-diagonal entries are unbounded operators.

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Boundedness of Some Convolution and Twisted Convolution Operators,We consider..—..boundedness problems for some special integral operators with oscillations both in the symbols and in the kernels.Such kernels have singularities on the unit sphere..and at infinity and are smooth on ℝ. ...The main purpose is to show how these features affect the boundedness picture.Some further problems are discussed.