Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
The paper deals with quarkonial decompositions and entropy numbers in weighted function spaces on hyperbolic manifolds. We use these results to develop a spectral theory of related Schrödinger operators in these hyperbolic worlds.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
179-202
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-07-03
poprawiono
1998-11-12
Twórcy
autor
- Mathematisches Institut, Fakultät für Mathematik und Informatik, Universität Jena, D-07740 Jena, Germany, triebel@minet.uni-jena.de
Bibliografia
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- [ET96] D. E. Edmunds and H. Triebel, Function Spaces, Entropy Numbers, Differential Operators, Cambridge Univ. Press, 1996.
- [EvH93] W. D. Evans and D. J. Harris, Fractals, trees and the Neumann Laplacian, Math. Ann. 296 (1993), 493-527.
- [Fal85] K. J. Falconer, The Geometry of Fractal Sets, Cambridge Univ. Press, 1985.
- [Fal90] K. J. Falconer, Fractal Geometry, Wiley, Chichester, 1990.
- [Har98] D. Haroske, Some logarithmic function spaces, entropy numbers, applications to spectral theory, Dissertationes Math. 373 (1998).
- [Har99] D. Haroske, Embeddings of some weighted function spaces on $ℝ^n$; entropy and approximation numbers, preprint, Jena, 1998.
- [HaT94] D. Haroske and H. Triebel, Entropy numbers in weighted function spaces and eigenvalue distributions of some degenerate pseudodifferential operators I, Math. Nachr. 167 (1994), 131-156.
- [HaT94*] D. Haroske and H. Triebel, Entropy numbers in weighted function spaces and eigenvalue distributions of some degenerate pseudodifferential operators II, ibid. 168 (1994), 109-137.
- [HeL97] C. Q. He and M. L. Lapidus, Generalized Minkowski content, spectrum of fractal drums, fractal strings and the Riemann zeta-function, Mem. Amer. Math. Soc. 608 (1997).
- [Lap91] M. L. Lapidus, Fractal drums, inverse spectral problems for elliptic operators and a partial resolution of the Weyl-Berry conjecture, Trans. Amer. Math. Soc. 325 (1991), 465-529.
- [Mat95] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Univ. Press, 1995.
- [RuS96] T. Runst and W. Sickel, Sobolev Spaces of Fractional Order, Nemytzkij Operators, and Nonlinear Partial Differential Equations, de Gruyter, Berlin, 1996.
- [Shu92] M. A. Shubin, Spectral theory of elliptic operators on non-compact manifolds, Astérisque 207 (1992), 35-108.
- [Skr96] L. Skrzypczak, Heat semi-group and function spaces on symmetric spaces of non-compact type, Z. Anal. Anwendungen 15 (1996), 881-899.
- [Skr97] L. Skrzypczak, Besov spaces on symmetric manifolds-the atomic decomposition, Studia Math. 124 (1997), 215-238.
- [Skr98] L. Skrzypczak, Atomic decompositions on manifolds with bounded geometry, Forum Math. 10 (1998), 19-38.
- [Skr98*] L. Skrzypczak, Mapping properties of pseudodifferential operators on manifolds with bounded geometry, J. London Math. Soc., to appear.
- [Stu93] K.-T. Sturm, On the $L^p$-spectrum of uniformly elliptc operators on Riemannian manifolds, J. Funct. Anal. 118 (1993), 442-453.
- [Tay89] M. E. Taylor, $L^p$-estimates on functions of the Laplace operator, Duke Math. J. 58 (1989), 773-793.
- [Tri83] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983.
- [Tri86] H. Triebel, Spaces of Besov-Hardy-Sobolev type on complete Riemannian manfolds, Ark. Mat. 24 (1986), 299-337.
- [Tri87] H. Triebel, Characterizations of function spaces on a complete Riemannian manifold with bounded geometry, Math. Nachr. 130 (1987), 312-346.
- [Tri88] H. Triebel, On a class of weighted function spaces and related pseudodifferential operators, Studia Math. 90 (1988), 37-68.
- [Tri92] H. Triebel, Theory of Function Spaces II, Birkhäuser, Basel, 1992.
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- [Tri98] H. Triebel, Decompositions of function spaces, in: Progress in Nonlinear Differential Equations Appl. 35, Birkhäuser, 1999, 691-730.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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