The regularity of measures and related properties of eigenfunctions and first eigenvalues of some fractal elliptic operators

• Autorzy: Triebel H.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with regularity properties of potentials of Radon measures u in IR^n, expressed in terms of some fractal quantities of u (Theorem 1). Based on these assertions, first eigenvalues and eigenfunctions of some fractal elliptic operators are considered (Theorems 2 and 3). The results are illustrated by examples.

Słowa kluczowe

EN

Radon measures; fractal quantities; Besov spaces; fractal elliptic operators; first eigenvalues; eigenfunctions

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr spec.
• Strony: 257--283
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Triebel H.

• Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, D-07740 Jena, Germany,

Bibliografia

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• [12] H. Triebel, Fractals and Spectra, Birkhäuser, Basel, 1997.
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• [14] H. Triebel, Fractal characteristics of measures; an approach via function spaces, Journ. Fourier Anal. Appl. 9 (2003), 411-430.
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• [16] H. Triebel, Approximation numbers in function spaces and the distribution of eigenvalues of some fractal elliptic operators, (submitted).
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Uwagi

Dedicated to Professor Musielak on the occasion of his 75th birthday.