메뉴 건너뛰기




Volumn 199, Issue , 1999, Pages 145-185

Fréchet algebra techniques for boundary value problems on noncompact manifolds: Fredholm criteria and functional calculus via spectral invariance

Author keywords

Boundary value problems; Boutet de Monvel's calculus; Fr chet algebras; Noncompact manifolds; Spectral invariance

Indexed keywords


EID: 0001115649     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19991990108     Document Type: Article
Times cited : (48)

References (50)
  • 1
    • 84972570335 scopus 로고
    • Characterization of pseudodifferential operators and applications
    • BEALS, R.: Characterization of Pseudodifferential Operators and Applications, Duke Math. Journal 44 (1977), 45-57, ibid. 46 (1979), pp. 215
    • (1977) Duke Math. Journal , vol.44 , pp. 45-57
    • Beals, R.1
  • 2
    • 84972570335 scopus 로고
    • BEALS, R.: Characterization of Pseudodifferential Operators and Applications, Duke Math. Journal 44 (1977), 45-57, ibid. 46 (1979), pp. 215
    • (1979) Duke Math. Journal , vol.46 , pp. 215
  • 3
    • 0001912013 scopus 로고
    • Boundary problems for pseudo - Differential operators
    • BOUTET DE MONVEL, L.: Boundary Problems for Pseudo - Differential Operators, Acta Math. 126 (1971), 11-51
    • (1971) Acta Math. , vol.126 , pp. 11-51
    • Boutet De Monvel, L.1
  • 4
    • 34250247250 scopus 로고
    • s,δ spaces on manifolds which are Euclidean at infinity
    • s,δ Spaces on Manifolds Which Are Euclidean at Infinity, Acta Math. 146 (1981), 129-150
    • (1981) Acta Math. , vol.146 , pp. 129-150
    • Choquet-Bruhat, Y.1    Christodoulou, D.2
  • 6
    • 0003243377 scopus 로고
    • The technique of pseudodifferential operators
    • Cambridge University Press, Cambridge, London, New York
    • CORDES, H.O.: The Technique of Pseudodifferential Operators, London Math. Soc. Lecture Notes 202, Cambridge University Press, Cambridge, London, New York, 1995
    • (1995) London Math. Soc. Lecture Notes , vol.202
    • Cordes, H.O.1
  • 7
    • 0005617464 scopus 로고
    • The N - th order elliptic boundary problem for noncompact boundaries
    • CORDES, H. O., and ERKIP, A. K.: The N - th Order Elliptic Boundary Problem for Noncompact Boundaries, Rocky Mountain J. Math. 10 (1980), 7-24
    • (1980) Rocky Mountain J. Math. , vol.10 , pp. 7-24
    • Cordes, H.O.1    Erkip, A.K.2
  • 10
    • 38249008655 scopus 로고
    • Normal solvability of boundary value problems on asymptotically flat manifolds
    • ERKIP, A. K., and SCHROHE, E.: Normal Solvability of Boundary Value Problems on Asymptotically Flat Manifolds, J. Funct. Anal. 109 (1992), 22-51
    • (1992) J. Funct. Anal. , vol.109 , pp. 22-51
    • Erkip, A.K.1    Schrohe, E.2
  • 11
    • 0001921094 scopus 로고
    • Relative inversion in der störungstheorie von operatoren und Ψ - Algebren
    • GRAMSCH, B.: Relative Inversion in der Störungstheorie von Operatoren und Ψ - algebren, Math. Annalen 269 (1984), 27-71
    • (1984) Math. Annalen , vol.269 , pp. 27-71
    • Gramsch, B.1
  • 13
    • 0013514080 scopus 로고
    • Decompositions of meromorphic Fredholm resolvents and Ψ* - Algebras
    • GRAMSCH, B., and KABALLO, W.: Decompositions of Meromorphic Fredholm Resolvents and Ψ* - Algebras, Integral Equations Op. Th. 12 (1989), 23-41
    • (1989) Integral Equations Op. Th. , vol.12 , pp. 23-41
    • Gramsch, B.1    Kaballo, W.2
  • 14
    • 0002980172 scopus 로고
    • Spectral invariance and submultiplicativity for Fréchet algebras with applications to pseudodifferential operators and Ψ* - Quantization
    • Birkhäuser, Boston, Basel
    • GRAMSCH, B., UEBERBERG, J., and WAGNER, K.: Spectral Invariance and Submultiplicativity for Fréchet Algebras with Applications to Pseudodifferential Operators and Ψ* - Quantization, Operator Theory: Advances and Applications 57, pp. 71-98, Birkhäuser, Boston, Basel, 1992
    • (1992) Operator Theory: Advances and Applications , vol.57 , pp. 71-98
    • Gramsch, B.1    Ueberberg, J.2    Wagner, K.3
  • 15
    • 0003279198 scopus 로고
    • Functional calculus for boundary value problems
    • Birkhäuser, Boston, Basel
    • GRUBB, G.: Functional Calculus for Boundary Value Problems, Progress in Mathematics 65, Birkhäuser, Boston, Basel, 1986
    • (1986) Progress in Mathematics , vol.65
    • Grubb, G.1
  • 16
    • 84973070968 scopus 로고
    • p spaces
    • p Spaces, Comm. in PDE 15 (1990), 289-340
    • (1990) Comm. in PDE , vol.15 , pp. 289-340
    • Grubb, G.1
  • 17
    • 51249167631 scopus 로고
    • p Sobolev spaces
    • p Sobolev Spaces, Math. Zeitschrift 218 (1995), 43-90
    • (1995) Math. Zeitschrift , vol.218 , pp. 43-90
    • Grubb, G.1
  • 18
    • 0000245727 scopus 로고
    • The transmission property
    • GRUBB, G., and HÖRMANDER, L.: The Transmission Property, Math. Scand. 67 (1990), 273-289
    • (1990) Math. Scand. , vol.67 , pp. 273-289
    • Grubb, G.1    Hörmander, L.2
  • 21
    • 0000028732 scopus 로고
    • A new proof of Weyl's formula on the asymptotic distribution of eigenvalues
    • GUILLEMIN, V.: A New Proof of Weyl's Formula on the Asymptotic Distribution of Eigenvalues, Advances Math. 55 (1985), 131-160
    • (1985) Advances Math. , vol.55 , pp. 131-160
    • Guillemin, V.1
  • 22
    • 0001515477 scopus 로고
    • Pseudodifferential operators and hypoelliptic equations
    • HÖRMANDER, L.: Pseudodifferential Operators and Hypoelliptic Equations, AMS Proceedings of Symp. Pure Math. 10 (1967) 138-183
    • (1967) AMS Proceedings of Symp. Pure Math. , vol.10 , pp. 138-183
    • Hörmander, L.1
  • 23
    • 0013482509 scopus 로고
    • Spectral invariance and the holomorphic functional calculus of J. L. Taylor in Ψ* - Algebras
    • LAUTER, R.: Spectral Invariance and the Holomorphic Functional Calculus of J. L. Taylor in Ψ* - Algebras J. Operator Theory 32 (1994), 311-329
    • (1994) J. Operator Theory , vol.32 , pp. 311-329
    • Lauter, R.1
  • 24
    • 0000487507 scopus 로고
    • Elliptic differential operators on noncompact manifolds
    • LOCKHART, R. B., and MCOWEN, R. C.: Elliptic Differential Operators on Noncompact Manifolds, Ann. Scuola Norm. Sup. Pisa, Ser. IV, Vol. XII (1985), 409-447
    • (1985) Ann. Scuola Norm. Sup. Pisa, Ser. IV , vol.12 , pp. 409-447
    • Lockhart, R.B.1    Mcowen, R.C.2
  • 25
    • 0001110758 scopus 로고
    • Transformation of boundary problems
    • MELROSE, R.: Transformation of Boundary Problems, Acta Math. 147 (1981), 149-236
    • (1981) Acta Math. , vol.147 , pp. 149-236
    • Melrose, R.1
  • 27
    • 0005615946 scopus 로고
    • Un problema ai limiti ellittico in un dominio non limitato
    • PARENTI, C.: Un problema ai Limiti Ellittico in un Dominio non Limitato, Annali Mat. Pura ed Appl. 93 (1972), 391-406
    • (1972) Annali Mat. Pura ed Appl. , vol.93 , pp. 391-406
    • Parenti, C.1
  • 28
    • 0041095297 scopus 로고
    • Pseudodifferential operators on a class of noncompact manifolds
    • RABINOVICH, V. S.: Pseudodifferential Operators on a Class of Noncompact Manifolds, Math. USSR Sb. 18 (1973), 45-59
    • (1973) Math. USSR Sb. , vol.18 , pp. 45-59
    • Rabinovich, V.S.1
  • 29
    • 0009249451 scopus 로고
    • The fredholm property of general boundary value problems on noncompact manifolds, and limit operators
    • RABINOVICH, V. S.: The Fredholm Property of General Boundary Value Problems on Noncompact Manifolds, and Limit Operators, Russian Acad. Sci. Dokl. Math. 46 (1993), 53-58
    • (1993) Russian Acad. Sci. Dokl. Math. , vol.46 , pp. 53-58
    • Rabinovich, V.S.1
  • 31
    • 0010833817 scopus 로고
    • Spaces of weighted symbols and weighted Sobolev spaces on manifolds
    • Pseudo - Differential Operators, CORDES, H. O., GRAMSCH, B., and WIDOM, H. (eds.), Springer - Verlag, Berlin, New York, Tokyo
    • SCHROHE, E.: Spaces of Weighted Symbols and Weighted Sobolev Spaces on Manifolds. In: Pseudo - Differential Operators, CORDES, H. O., GRAMSCH, B., and WIDOM, H. (eds.), Springer LN Math. 1256, pp. 360-377, Springer - Verlag, Berlin, New York, Tokyo, 1987
    • (1987) Springer LN Math. , vol.1256 , pp. 360-377
    • Schrohe, E.1
  • 32
    • 0013299372 scopus 로고
    • A Ψ* - Algebra of pseudodifferential operators on noncompact manifolds
    • SCHROHE, E.: A Ψ* - Algebra of Pseudodifferential Operators on Noncompact Manifolds, Arch. Math. 51 (1988), 81-86
    • (1988) Arch. Math. , vol.51 , pp. 81-86
    • Schrohe, E.1
  • 33
    • 0005518465 scopus 로고
    • Complex powers on noncompact manifolds and manifolds with singularities
    • SCHROHE, E.: Complex Powers on Noncompact Manifolds and Manifolds with Singularities, Math. Ann. 281 (1988), 393-409
    • (1988) Math. Ann. , vol.281 , pp. 393-409
    • Schrohe, E.1
  • 35
    • 0041095295 scopus 로고
    • Spectral invariance, ellipticity, and the Fredholm property for pseudodifferential operators on weighted Sobolev spaces
    • SCHROHE, E.: Spectral Invariance, Ellipticity, and the Fredholm Property for Pseudodifferential Operators on Weighted Sobolev Spaces, Ann. Global Anal. Geom. 10 (1992), 237-254
    • (1992) Ann. Global Anal. Geom. , vol.10 , pp. 237-254
    • Schrohe, E.1
  • 36
    • 0039315914 scopus 로고
    • Functional calculus and Fredholm criteria for boundary value problems on noncompact manifolds
    • Birkhäuser, Boston, Basel
    • SCHROHE, E.: Functional Calculus and Fredholm Criteria for Boundary Value Problems on Noncompact Manifolds. In: Proceedings Lambrecht Dec. 991, Operator Theory: Advances and Applications 57, 271-289, Birkhäuser, Boston, Basel, 1992
    • (1992) Proceedings Lambrecht Dec. 991, Operator Theory: Advances and Applications , vol.57 , pp. 271-289
    • Schrohe, E.1
  • 37
    • 0039753396 scopus 로고
    • A characterization of the singular green operators in Boutet de Monvel's calculus via wedge Sobolev spaces
    • SCHROHE, E.: A Characterization of the Singular Green Operators in Boutet de Monvel's Calculus via Wedge Sobolev Spaces, Comm. Part. Diff. Eq. 19 (1994), 677-699
    • (1994) Comm. Part. Diff. Eq. , vol.19 , pp. 677-699
    • Schrohe, E.1
  • 44
    • 84966198903 scopus 로고
    • ∞ functions defined in a half space
    • ∞ Functions Defined in a Half Space, Proceedings AMS 15 (1964), 625-626
    • (1964) Proceedings AMS , vol.15 , pp. 625-626
    • Seeley, R.T.1
  • 46
    • 0002117637 scopus 로고
    • The analytic functional calculus for several commuting operators
    • TAYLOR, J. L.: The Analytic Functional Calculus for Several Commuting Operators, Acta Math. 125 (1970), 1-38
    • (1970) Acta Math. , vol.125 , pp. 1-38
    • Taylor, J.L.1
  • 48
    • 0039662686 scopus 로고
    • Normally solvable problems for elliptic systems in equations of convolution
    • VISHIK, M. I., and ESKIN, G. I.: Normally Solvable Problems for Elliptic Systems in Equations of Convolution, Math. USSR Sb. 14, (116) (1967), 326-356
    • (1967) Math. USSR Sb. , vol.14 , Issue.116 , pp. 326-356
    • Vishik, M.I.1    Eskin, G.I.2
  • 49
    • 0003239399 scopus 로고
    • Topological vector spaces and algebras
    • Springer -Verlag, Berlin, Heidelberg, New York
    • WAELBROECK. L.: Topological Vector Spaces and Algebras, Springer LN Math. 230, Springer -Verlag, Berlin, Heidelberg, New York, 1971
    • (1971) Springer LN Math. , vol.230
    • Waelbroeck, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.