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Excursion to Functional Analysis

In: An Introduction to Modern Analysis

Author

Listed:
  • Vicente Montesinos

    (Universitat Politècnica de València, Departamento de Matemática Aplicada Instituto de Matemática Pura y Aplicada)

  • Peter Zizler

    (Mount Royal University, Department of Mathematics, Physics and Engineering)

  • Václav Zizler

    (University of Alberta, Department of Mathematical and Statistical Sciences)

Abstract

In modern analysis, most of the problems in science and engineering have solutions in infinite-dimensional spaces of functions, where closed bounded sets are usually not compact, the measure theory is of limited use, linear operators may not have eigenvalues even in the complex case, or even reasonable continuous functions do not attain their extrema on closed bounded sets, just to mention some difficulties. Thus we encounter there problems additional to those we handled in the first chapters of this text. Functional analysis helps in solving these problems by providing additional powerful tools that work in general contexts, allowing in this way to treat a large variety of situations looking at them from a unifying point of view.

Suggested Citation

  • Vicente Montesinos & Peter Zizler & Václav Zizler, 2015. "Excursion to Functional Analysis," Springer Books, in: An Introduction to Modern Analysis, edition 127, chapter 11, pages 505-615, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12481-0_11
    DOI: 10.1007/978-3-319-12481-0_11
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