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Toeplitz matrices with variable coefficients, pseudodifferential operators, and Strichartz's method

✍ Scribed by Eugene Shargorodsky

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
156 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We present simple proofs of sharp uniform boundedness results for sequences of Toeplitz matrices with variable coefficients. These proofs are based on Strichartz's method which reduces the problem of boundedness of operators “with variable coefficients” to the same problem for operators that have “constant coefficients” but act on Hilbert space valued functions. The paper also contains counterexamples showing the optimality of the boundedness results obtained with the help of Strichartz's method and a brief discussion of similar results for pseudodifferential operators (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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✍ WiesŁaw MarszaŁek 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 243 KB

This paper presents a new method of piecewise-constant solution of bilinear statespace equations. The method is based on Picard's iterative algorithm and block-pulse operational matrices for integration and convolution. An illustrative example is given.