Trace formulas for some singular differential operators and applications

Mathematische Nachrichten

Volumn 211, Issue , 2000, Pages 127-157

  Metafune, Giorgio ^a   Pallara, Diego ^a  

^a UNIVERSITY OF SALENTO   (Italy)

Author keywords

Eigenvalues; Singular differential operators

Indexed keywords

EID: 0034366438     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1522-2616(200003)211:1<127::AID-MANA127>3.0.CO;2-A     Document Type: Article

References (29)

1. ANGENENT, S.: Local Existence and Regularity for a Class of Degenerate Parabolic Equations, Math. Ann. 280 (1988), 465-482
2. p, Diff. Int. Eqs. 7 (1994), 1153-1168
3. BARBU, V., and FAVINI, A.: The Analytic Semigroup Generated by a Second Order Degenerate Differential Operator in C([0, 1]), Rend. Circ. Mat. Palermo s.II 52 (1998), 23-42
4. CAMPITI, M., and METAFUNE, G.: Ventcel's Boundary Conditions and Analytic Semigroups, Arch. Math. 70 (1998), 377-390
5. CAMPITI, M., METAFUNE, G., and PALLARA, D.: Degenerate Self-Adjoint Evolution Equations on the Unit Interval, Semigroup Forum 57 (1998), 1-36
6. CAMPITI, M., METAFUNE, G., and PALLARA, D.: Feller Semigroups with Reflecting Barriers, J. Math. Anal. and Appl., to appear
7. CAMPITI, M., METAFUNE, G., PALLARA, D., and ROMANELLI, S.: Semigroups for Ordinary Differential Operators, Section VI.4. In: K. ENGEL, R. NAGEL: One-Parameter Semigroups for Linear Evolution Equations, Springer Graduate Texts in Mathematics 194 (1999)
8. n with Coefficients Having Polynomial Growth, Commun. in Partial Differential Equations 21 (1996), 281-317
9. 0-Semigroups Generated by Differential Operators Satisfying Ventcel's Boundary Conditions, Indag. Math. 89 (1986), 379-387
10. DA PRATO, G., and LUNARDI, A.: On the Ornstein-Uhlenbeck Operator in Spaces of Continuous Functions, J. Funct. Anal. 131 (1995), 94-114
11. DA PRATO, G., and ZABCZYK, J.: Ergodicity for Infinite Dimensional Systems, Cambridge U. P., 1996
12. DAVIES, E. B.: Heat Kernels and Spectral Theory, Cambridge U. P., 1989
13. DAVIES, E. B.: Spectral Theory and Differential Operators, Cambridge U. P., 1995
14. DAVIES, E. B., and SIMON, B.: Ultracontractivity and the Heat Kernel for Schrödinger Operators and Dirichlet Laplacians, J. Funct. Anal. 59 (1984), 335-395
15. 1 Properties of Intrinsic Schrödinger Semigroups, J. Funct. Anal. 65 (1986), 126-146
16. EDMUNDS, D.E., GURKA, P., and PICK, L.: Compactness of Hardy-Type Integral Operators in Weighted Banach Function Spaces, Studia Math. 109 (1994), 73-90
17. EVERITT, W., KWONG, M., and ZETTL, A.: Differential Operators and Quadratic Inequalities with a Degenerate Weight, J. Math. Anal. and Appl. 98 (1984), 378-399
18. FELLER, W.: The Parabolic Differential Equations and the Associated Semi-Groups of Transformations, Ann. of Math. 55 (1952), 468-519
19. FELLER, W.: Diffusion Processes in One Dimension, Trans. Am. Math. Soc. 97 (1954), 1-31
20. KAC, I. S., and KREǏN, M. G.: Criteria for the Discretness of the Spectrum of a Singular String, Izv. Vysš. Učebn. Zaved. Matematika 2 (3)(1958), 136-153, (in Russian); M. R. 25# 3232
21. KAC, I. S., and KREǏN, M. G.: On the Spectral Functions of the String, Amer. Math. Soc. Transl. 103 (1974), 19-102
22. Mandl, P.: Analytical Treatment of One-Dimensional Markov Processes, Springer-Verlag, 1968
23. MAZ'JA, V. G.: Sobolev Spaces, Springer-Verlag, 1985
24. METAFUNE, G.: Analyticity for Some Degenerate One-Dimensional Evolution Equations, Studia Math. 127 (1998), 251-276
25. p-Spectrum of Ornstein-Uhlenbeck Operators, preprint
26. VAN NEERVEN, J. M. A. M., and ZABCZYK, J.: Norm Discontinuity of Ornstein-Uhlenbeck Semigroups, Semigroup Forum 59 (1999), 389-403
27. NIESSEN, H. D., and ZETTL, D.: Singular Sturm-Liouville Problems: the Friedrichs Extension and Comparison of Eigenvalues, Proc. London Math. Soc. 64 (1992), 545-578
28. OLVER, F. W. J.: Asymptotics and Special Functions, Peters, 1997
29. RIESZ, F., and NAGY, B. Sz.: Functional Analysis, Ungar, 1955 and Dover, 1990