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Unbounded Operators on Hilbert Space

In: Basic Classes of Linear Operators

Author

Listed:
  • Israel Gohberg

    (Tel Aviv University, School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences)

  • Seymour Goldberg

    (University of Maryland, Department of Mathematics)

  • Marinus A. Kaashoek

    (Vrije Universiteit Amsterdam, Department of Mathematics and Computer Science)

Abstract

The theory developed thus far concentrated on bounded linear operators on a Hilbert space which had applications to integral equations. However, differential equations give rise to an important class of unbounded linear operators which are not defined on all of L2([a, b]). In this chapter an introduction to unbounded operators is presented which includes the spectral theorem for the Sturm-Liouville operator. Simple examples of the spectral theory of unbounded self adjoint operators are also given. For a more detailed theory the reader is referred to [G], [GGK1], [K] and [DS2].

Suggested Citation

  • Israel Gohberg & Seymour Goldberg & Marinus A. Kaashoek, 2003. "Unbounded Operators on Hilbert Space," Springer Books, in: Basic Classes of Linear Operators, chapter 0, pages 203-217, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7980-4_6
    DOI: 10.1007/978-3-0348-7980-4_6
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