×

zbMATH — the first resource for mathematics

Pseudodifferential operators on stratified manifolds. (English. Russian original) Zbl 1133.58023
Differ. Equ. 43, No. 4, 536-549 (2007); translation from Differ. Uravn. 43, No. 4, 519-532 (2007).
The aim of the study is to describe a class of zero-order pseudodifferential operators related to differential operators with degeneration of first order with respect to the distance to the strata on a stratified manifold. The paper contains auxiliary results related to the localization principles for abstract local operators. It is announced that the results about the pseudodifferential operators will be published in the second part of the paper.

MSC:
58J40 Pseudodifferential and Fourier integral operators on manifolds
35S35 Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc.
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Egorov, Yu. and Schulze, B.-W., Pseudo-Differential Operators, Singularities, Applications, Basel: Birkhäuser, 1997. · Zbl 0877.35141
[2] Schulze, B.-W., Pseudodifferential Operators on Manifolds with Singularities, Amsterdam: North-Holland, 1991.
[3] Calvo, D., Martin, C.-I., and Schulze, B.-W., in RIMS Conf. Dedicated to L. Boutet de Monvel on Microlocal Analysis and Asymptotic Analysis, Kyoto, August, 2004, Tokyo, 2005, pp. 22–35.
[4] Melrose, R., in Partial Differential Equations and Mathematical Physics (Copenhagen, 1995; Lund, 1995), Boston: Birkhäuser, 1996, pp. 246–261.
[5] Nistor, V., in Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, Providence: AMS, 2005, pp. 307–328. · Zbl 1091.58017
[6] Plamenevskii, B.A. and Senichkin, V.N., Algebra i Analiz, 2001, vol. 13, no. 6, pp. 124–174.
[7] Antonevich, A. and Lebedev, A., Functional-Differential Equations. I. C*-Theory, Harlow: Longman, 1994. · Zbl 0799.34001
[8] Gohberg, I. and Krupnik, N., One-Dimensional Linear Singular Integral Equations. I. Introduction, Basel: Birkhäuser, 1992.
[9] Simonenko, I.B., Izv. Akad. Nauk SSSR Ser. Mat., 1965, vol. 29, no. 3, pp. 567–586; no. 4, pp. 757–782.
[10] Vasilevskii, N.L., in Linear Operators in Function Spaces. Abstracts of the North Caucasus Regional Conf., Groznyi, 1989, pp. 32–33.
[11] Vasilevski, N., Integral Equations Operator Theory, 1994, vol. 19, no. 3, pp. 327–348. · Zbl 0829.43006 · doi:10.1007/BF01203669
[12] Nazaikinskii, V.E., Savin, A.Yu., Sternin, B.Yu., and Schulze, B.-W., Dokl. Akad. Nauk, 2005, vol. 402, no. 6, pp. 743–747.
[13] Atiyah, M.F., in Proc. of the Int. Symposium on Functional Analysis, Tokyo: University of Tokyo Press, 1969, pp. 21–30.
[14] Dixmier, J., Les C*-algèbres et leurs représentations, Paris: Gauthier-Villars, 1969. · Zbl 0174.18601
[15] Arveson, W., An Invitation to C*-Algebras, New York; Heidelberg; Berlin: Springer-Verlag, 1976. · Zbl 0344.46123
[16] Plamenevskii, B.A. and Senichkin, V.N., Izv. Akad. Nauk SSSR Ser. Mat., 1987, vol. 51, no. 4, pp. 833–859.
[17] Dauns, J. and Hofmann, K.H., Representation of Rings by Sections, Providence: AMS, 1968. · Zbl 0174.05703
[18] Yosida, K., Functional Analysis, New York: Springer-Verlag, 1968. · Zbl 0830.46001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.