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We study a system of pseudodifferential equations which is elliptic in the Petrovskiî sense on a closed smooth manifold. We prove that the operator generated by the system is a Fredholm operator in a refined two-sided scale of Hilbert function spaces. Elements of this scale are special isotropic spaces of Hörmander-Volevich-Paneah.
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Rocznik
Tom
Strony
213--224
Opis fizyczny
Bibliogr. 25 poz.
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autor
autor
Bibliografia
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- [3] M. F. Atiyah and I. M. Singer, The index of elliptic operators on compact manifolds, Bull. Amer. Math. Soc. 69 (1963), 422-433.
- [4] Yu. M. Berezanskij, Expansions in Eigenfunctions of Selfadjoint Operators, Transl. Math. Monogr. 17, Amer. Math. Soc., Providence, 1968.
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- [6] W. Farkas and H.-G. Leopold, Characterisations of function spaces of generalized smoothness, Ann. Mat. Pura Appl. 185 (2006), 1-62.
- [7] C. Foiaş. et J.-L. Lions, Sur certains théorèmes d’interpolation. Acta Sci. Math. (Szeged) 22 (1961), 269-282.
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- [9] L. Hörmander, Linear Partial Differential Operators, Springer, Berlin, 1963.
- [10] —, The Analysis of Linear Partial Differential Operators. II. Differential Operators with Constant Coefficients, Springer, Berlin, 1983.
- [11] —, The Analysis of Linear Partial Differential Operators. III. Pseudo-Differential Operators, Springer, Berlin, 1985.
- [12] G. A. Kalyabin and P. I. Lizorkin, Spaces of functions of generalized smoothness, Math. Nachr. 133 (1987), 7-32.
- [13] V. A. Mikhailets, Asymptotics of the spectrum of elliptic operators and boundary conditions, Soviet Math. Dokl. 26 (1982), 464-468.
- [14] —, A precise estimate of the remainder in the spectral asymptotics of general elliptic boundary problems, Funct. Anal. Appl. 23 (1989), 137-139.
- [15] V. A. Mikhailets and A. A. Murach, Improved scale of spaces and elliptic boundary-value problems. I, Ukrainian Math. J. 58 (2006), 244-262.
- [16] —, —, Improved scale of spaces and elliptic boundary-value problems. II, ibid., 398-417.
- [17] —, —, Regular elliptic boundary-value problem for a homogeneous equation in a two-sided refined scale of spaces, ibid., 1748-1767.
- [18] —, —, Elliptic operator with homogeneous regular boundary conditions in two-sided refined scale of spaces, Ukrainian Math. Bull. 3 (2006), 529-560.
- [19] —, —, Refined scale of spaces and elliptic boundary-value problems. III, Ukrainian Math. J. 59 (2007), 744-765.
- [20] —, —, An elliptic boundary-value problem in a two-sided refined scale of spaces, Ukrain. Mat. Zh. 60 (2008), 497-520 (in Russian).
- [21] —, —, Interpolation with a function parameter and refined scale of spaces, Methods Funct. Anal. Topology 14 (2008), 81-100.
- [22] A. A. Murach, Elliptic pseudo-differential operators in a refined scale of spaces on a closed manifold, Ukrainian Math. J. 59 (2007), 874-893.
- [23] B. Paneah, The Oblique Derivative Problem. The Poincare Problem, Wiley - VCH, Berlin, 2000.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0035-0004