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On the Reduction of Linear Systems Related to Boundary Value Problems

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Operator Theory, Pseudo-Differential Equations, and Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 228))

Abstract

The main topic of this work is the investigation of operator relations which appear during the reduction of linear systems, particularly in the study of boundary value problems. The first objective is to improve formulations like “equivalent reduction” by the help of operator relations. Then we describe how some of these operator relations can be employed to determine the regularity class and effective solution of boundary value problems. Furthermore operator relations are used to put boundary value problems into a correct space setting, e.g., by operator normalization.

Mathematics Subject Classification (2010). Primary 35K35; Secondary 35G15, 58J35.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais, P-1049-001, Lisboa, Portugal

    Frank-Olme Speck

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  1. Frank-Olme Speck
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Correspondence to Frank-Olme Speck .

Editor information

Editors and Affiliations

  1. de Morelos, Facultad de Ciencias, Universidad Autónoma del Estado, Av. Universidad 1001, Col. Chamilpa, Cuernavaca, 62209, Morelos, Mexico

    Yuri I. Karlovich

  2. , Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, Torino, 10123, Italy

    Luigi Rodino

  3. , Fakultät für Mathematik, Technische Universität Chemnitz, Reichenhainer Straße 39, Chemnitz, 09126, Germany

    Bernd Silbermann

  4. , Department of Mathematics, College of William and Mary, Jones Hall 114, Williamsburg, 23187-8795, Virginia, USA

    Ilya M. Spitkovsky

Additional information

To Vladimir Rabinovich on the occasion of his 70th birthday

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Speck, FO. (2013). On the Reduction of Linear Systems Related to Boundary Value Problems. In: Karlovich, Y., Rodino, L., Silbermann, B., Spitkovsky, I. (eds) Operator Theory, Pseudo-Differential Equations, and Mathematical Physics. Operator Theory: Advances and Applications, vol 228. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0537-7_20

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