Download Advances in Structured Operator Theory and Related Areas: by M. A. Kaashoek (auth.), Marinus A. Kaashoek, Leiba Rodman, PDF

By M. A. Kaashoek (auth.), Marinus A. Kaashoek, Leiba Rodman, Hugo J. Woerdeman (eds.)

This quantity is devoted to Leonid Lerer at the celebration of his 70th birthday. the most half provides contemporary ends up in Lerer’s study niche, including Toeplitz, Toeplitz plus Hankel, and Wiener-Hopf operators, Bezout equations, inertia variety effects, matrix polynomials, and similar parts in operator and matrix thought. Biographical fabric and Lerer's checklist of courses whole the volume.

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Extra info for Advances in Structured Operator Theory and Related Areas: The Leonid Lerer Anniversary Volume

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He helped me to choose more profitable results for the presentation, to build the report in the right form, to provide possible questions. Many times I run tutorials in the courses where Leonid taught. Students appreciated Leonid as a lecturer very much. I heard from students that they liked his explanations, liked his logical and consistent presentation of material, illustrated with many examples and solved problems. Working with Leonid as his teaching assistant I acquired wide experience for my future professional life.

1 ????(????, ????1 )????1 + ⋅ ⋅ ⋅ + ???????? ????(????, ???????? )???????? . ???????? ???????? Then a standard reproducing-kernel computation gives us that ????????∗ : ℋ(????) → ℂ???? is given by ⎤ ⎡ ⟨???? (????1 ), ????1 ⟩???? ⎥ ⎢ .. ????????∗ : ???? → ⎣ ⎦ . 6) and x ∈ ℂ???? , find ???? ∈ ℋ(????) (possibly also with ∥???? ∥ℋ(????) ≤ 1) so that ????????∗ ???? = x. We now formulate our abstract left tangential Nevanlinna–Pick interpolation problem as follows. Let ????(????, ????) be an ℒ(????)-valued positive kernel on a Cartesian product set Ω×Ω and let ℋ(????) be the associated reproducing kernel Hilbert space, that is, the unique inner product space of ????-valued functions on Ω that contains the functions ???? → ???????? (????) := ????(????, ????)???? for all fixed ???? ∈ Ω and ???? ∈ ???? which in turn have the reproducing property for ℋ(????): ⟨????, ???????? ????⟩ℋ(????) = ⟨???? (????), ????⟩???? for all ???? ∈ ℋ(????).

4. 3 (ii) has a solution if and only if ???? ≥ xx∗ , where ???? := ????????∗ ???????? . 3 (i) has a solution if and only if x ∈ Ran ???? 2 . A. Ball and V. Bolotnikov Proof. 1) necessarily have the form of a multiplication operator ???????? for some function ???? ∈ ℋ(????). 8). 8), Ran ???? 2 = Ran ????????∗ . 3. □ Let us assume that the operator ???? = ????????∗ ???????? is strictly positive definite. 10) is isometrically included in ℋ(????). Moreover, the orthogonal complement of ???? in ˜ with reproducing kernel ℋ(????) is the reproducing kernel Hilbert space ℋ(????) ˜ ????) = ????(????, ????) − ???? (????)???? −1 ???? (????)∗ .

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