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Correlation Functions of Intrinsically Stationary Random Fields

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Modern Analysis and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 190))

Abstract

In the introduction we give a short historical survey on the theory of correlation functions of intrinsically stationary random fields. We then prove the existence of generalized correlation functions for intrinsically stationary fields on ℝd as well as an integral representation for these functions. At the end of the paper we show that intrinsically stationary fields are related to unitary operators in Pontryagin spaces in a similar way as stationary fields are related to unitary operators in Hilbert spaces.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technical University of Dresden, Mommsenstr. 13, 01062, Dresden, Germany

    Zoltán Sasvári

Authors
  1. Zoltán Sasvári
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Vadim M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    Israel Gohberg

  3. Institute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivska st., 01601, Kyiv-4, Ukraine

    Anatoly Kochubei , Yurij Berezansky , Myroslav Gorbachuk  & Valentyna Gorbachuk , ,  & 

  4. Department of Mathematical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Gennadiy Popov

  5. Institute of Analysis and Scientific Computing, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Heinz Langer

Additional information

Dedicated to the Centenary of Mark Grigorievich Krein

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Sasvári, Z. (2009). Correlation Functions of Intrinsically Stationary Random Fields. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 190. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9919-1_28

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