|
An algebraic approach to multiparameter spectral theory
Author(s):
Luzius
Grunenfelder;
Tomaz
Kosir
Journal:
Trans. Amer. Math. Soc.
348
(1996),
2983-2998.
MSC (1991):
Primary 16W30, 35P10, 47A13
MathSciNet review:
1361640
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Root subspaces for multiprameter eigenvalue problems are described using coalgebraic techniques. An algorithm is given to construct bases for the root subspaces.
References:
- 1.
- E. Abe. Hopf Algebras. Cambridge Univ. Press, 1980. MR 83a:16010
- 2.
- M.S. Almamedov and G.A. Isaev. Solvability of Nonselfadjoint Linear Operator Systems, and the Set of Decomposability of Multiparameter Spectral Problems. Soviet. Math. Dokl., 31:472--474, 1985. MR 87b:47018 (Russian original)
- 3.
- F.M. Arscott. Periodic Differential Equations. Pergamon Press : Oxford, 1964. MR 30:4066
- 4.
- F.V. Atkinson. Multiparameter Spectral Theory. Bull. Amer. Math. Soc., 74:1--27, 1968. MR 36:3145
- 5.
- F.V. Atkinson. Multiparameter Eigenvalue Problems. Academic Press, 1972. MR 56:9291
- 6.
- P.A. Binding. Multiparameter Root Vectors. Proc. Edin. Math. Soc., 32:19--29, 1989. MR 90a:47048
- 7.
- P.A. Binding and P.J. Browne. Two Parameter Eigenvalue Problems for Matrices. Lin. Alg. Appl., 113:139--157, 1989. MR 89m:47012
- 8.
- P.A. Binding and T. Ko\v{s}ir. Second Root Vectors for Multiparameter Eigenvalue Problems of Fredholm Type, Trans. Amer. Math. Soc. 348: 229--249, 1996.
- 9.
- P.A. Binding and K. Seddighi. Elliptic Multiparameter Eigenvalue Problems. Proc. Edin. Math. Soc., 30:215--228, 1987. MR 88g:47036
- 10.
- M. Faierman. Two-parameter Eigenvalue Problems in Ordinary Differential Equations, volume 205 of Pitman Research Notes in Mathematics. Longman Scientific and Technical, U.K., 1991. MR 93b:47095
- 11.
- G.A. Gadzhiev. On a Multitime Equation and its Reduction to a Multiparameter Spectral Problem. Soviet. Math. Dokl., 32:710--713, 1985. MR 87j:35365 (Russian original)
- 12.
- G.A. Gadzhiev. Introduction to Multiparameter Spectral Theory. Azerbaijan State University, Baku, 1987. (Russian)
- 13.
- L. Grunenfelder and T. Ko\v{s}ir. Representation of Commuting Maps by Tensor Products, preprint.
- 14.
- L. Grunenfelder and M. Omladi\v{c}. Linearly Recursive Sequences and Operator Polynomials. Lin. Alg. Appl., 182:127--145, 1993. MR 93m:16027
- 15.
- L. Grunenfelder and R. Paré. Families Parametrized by Coalgebras. J. Algebra, 107:316--375, 1987. MR 88i:16044
- 16.
- G.A. Isaev. On Root Elements of Multiparameter Spectral Problems. Soviet. Math. Dokl., 21:127--130, 1980. MR 82c:47021 (Russian original)
- 17.
- H.(G.A.) Isaev. Lectures on Multiparameter Spectral Theory. Dept. of Math. and Stats., University of Calgary, 1985.
- 18.
- A. Källström and B.D. Sleeman. Solvability of a Linear Operator System. J. Math. Anal. Appl., 55:785--793, 1976. MR 54:5881
- 19.
- T. Ko\v{s}ir. The Finite-dimensional Multiparameter Spectral Theory : The Nonderogatory Case. Lin. Alg. Appl., 212/213:45--70, 1994. MR 95k:15020
- 20.
- T. Ko\v{s}ir. Commuting Matrices and Multiparameter Eigenvalue Problems. PhD thesis, Dept. of Math. and Stats., University of Calgary, 1993.
- 21.
- J.W. Milnor and J.C. Moore. On the Structure of Hopf Algebras. Ann. of Math., 81:211--264, 1965. MR 30:4259
- 22.
- B. Peterson and E. Taft. The Hopf Algebra of Linearly Recursive Sequences. Aequationes Math., 20:1--17, 1980. MR 81j:16012
- 23.
- B.D. Sleeman. Multiparameter Spectral Theory in Hilbert Space, volume 22 of Pitman Research Notes in Mathematics. Pitman, London, Belmont, 1978. MR 81h:47004
- 24.
- B.D. Sleeman. Review of [10]. SIAM Review , 34:684--687, 1992.
- 25.
- M.E. Sweedler. Hopf Algebras . Benjamin, New York, 1969. MR 40:5705
- 26.
- H. Volkmer. On the Completeness of Eigenvectors of Right Definite Multiparameter Problems. Proc. Roy. Soc. Edin. , 96A:69--78, 1984. MR 86a:47014
- 27.
- H. Volkmer. Multiparameter Eigenvalue Problems and Expansion Theorems , volume 1356 of Lecture Notes in Mathematics . Springer-Verlag, Berlin, New York, 1988. MR 91d:47021
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (1991):
16W30, 35P10, 47A13
Retrieve articles in all Journals with
MSC (1991):
16W30, 35P10, 47A13
Additional Information:
Luzius
Grunenfelder
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Email:
luzius@cs.dal.ca
Tomaz
Kosir
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, 61000 Ljubljana, Sloevenia
Email:
tkosir@fmf.uni-lj.si
DOI:
10.1090/S0002-9947-96-01679-0
PII:
S 0002-9947(96)01679-0
Received by editor(s):
May 2, 1994
Copyright of article:
Copyright
1996,
American Mathematical Society
|