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Restriction, Localization and Microlocalization

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Quadrature Domains and Their Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 156))

Abstract

We discuss methods for studying quadrature domains for subharmonic functions, using three modifications of measures, which we call restriction, localization, and microlocalization. Applying these methods, we discuss the shape of the blob in the Hele-Shaw flow free-boundary problem.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo, 192-0397, Japan

    Makoto Sakai

Authors
  1. Makoto Sakai
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093, USA

    Peter Ebenfelt

  2. Department of Mathematics, Royal Institute of Technology (KTH), 100 44, Stockholm, Sweden

    Björn Gustafsson

  3. Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701, USA

    Dmitry Khavinson

  4. Mathematics Department, University of California, Santa Barbara, Santa Barbara, CA, 93106, USA

    Mihai Putinar

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Sakai, M. (2005). Restriction, Localization and Microlocalization. In: Ebenfelt, P., Gustafsson, B., Khavinson, D., Putinar, M. (eds) Quadrature Domains and Their Applications. Operator Theory: Advances and Applications, vol 156. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7316-4_9

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