Approximate Diagonal Integral Representations and Eigenmeasures for Lipschitz Operators on Banach Spaces

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ERDOĞAN E., Sanchez Perez E. A.

MATHEMATICS, cilt.10, sa.2, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3390/math10020220
  • Dergi Adı: MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: eigenmeasure, operators, banach space, eigenvalue, spectral function, NONLINEAR EIGENVALUE PROBLEMS
  • Marmara Üniversitesi Adresli: Evet

Özet

A new stochastic approach for the approximation of (nonlinear) Lipschitz operators in normed spaces by their eigenvectors is shown. Different ways of providing integral representations for these approximations are proposed, depending on the properties of the operators themselves whether they are locally constant, (almost) linear, or convex. We use the recently introduced notion of eigenmeasure and focus attention on procedures for extending a function for which the eigenvectors are known, to the whole space. We provide information on natural error bounds, thus giving some tools to measure to what extent the map can be considered diagonal with few errors. In particular, we show an approximate spectral theorem for Lipschitz operators that verify certain convexity properties.