Popivanov, P. R. A link between small divisors and smoothness of the solutions of a class of partial differential operators. (English) Zbl 0529.35019 Ann. Global Anal. Geom. 1, No. 3, 77-92 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 Documents MSC: 35H10 Hypoelliptic equations 35A30 Geometric theory, characteristics, transformations in context of PDEs 46F05 Topological linear spaces of test functions, distributions and ultradistributions Keywords:small divisors; smoothness of the solutions; global hypoellipticity; Schwartz space of tempered distributions; variable multiplicity of the characteristics; microlocal hypoellipticity PDFBibTeX XMLCite \textit{P. R. Popivanov}, Ann. Global Anal. Geom. 1, No. 3, 77--92 (1983; Zbl 0529.35019) Full Text: DOI References: [1] Antosik, P., Mikusinski, Z., Sicorski, R.: ”Theory of distributions” Polish Scientific Publishers, Warszawa, 1973. · Zbl 0267.46028 [2] Baker, A.: ”Transcendental number theory”, Cambridge University Press, 1975. · Zbl 0297.10013 [3] Duistermaat, J., Hörmander, L.: ”Fourier integral operators”, II, Acta Math., 128:3,4 (1972), 193–269. · Zbl 0232.47055 · doi:10.1007/BF02392165 [4] Grusin, V.V.: ”On a class of hypoelliptic operators”, Math. USSR Sbornik, 12:3 (1970). [5] Guillemin, V., Schaeffer, D.: ”On a certain class of Fuchsian partial differential equations”, Duke Math. J., 44:1 (1977), 157–199. · Zbl 0356.35080 · doi:10.1215/S0012-7094-77-04408-8 [6] Hörmander, L.: ”Pseudodifferential operators and non-elliptic boundary problems”, Ann. of Math., 83:1 (1966) · Zbl 0132.07402 [7] Hörmander, L.: ”Fourier integral operators”, I , Acta Math., 127:1,2 (1971). · Zbl 0212.46601 [8] Hörmander, L.: ”A class of hypoelliptic pseudodiff. operators with double characteristics”, Math. Ann., 217:2 (1975). · Zbl 0306.35032 [9] Ivrii, V.: ”Wave front sets of the solutions of some pseudo-differential operators, Trudy Moskov. Math. Obsc., 39 (1979), 49–82, (Russian). [10] de Monvel, L. B.: ”Hypoelliptic operators with double characteristics and related pseudodiff. operators”, Comm. Pure Appl. Math., 27:5 (1974). · Zbl 0294.35020 [11] Popivanov, P.: ”Some classes of partial differential operators with multiple characteristics, having no solution” (Russian), Pliska, Studia Math. Bulg., 3 (1981), 47–61. · Zbl 0497.35018 [12] Sansone, G.: ”Orthogonal functions”, Interscience Publishers, N. Y., 1959. · Zbl 0084.06106 [13] Schwartz, L.: ”Théorie des distributions”, I , Paris, 1950; Paris 1951. · Zbl 0037.07301 [14] Sjöstrand, J.: ”Parametrices for pseudodiff. operators with multiple characteristics”, Ark. för Mat., 12:1 (1974). · Zbl 0317.35076 [15] Subin, M. ”Pseudodifferential operators and spectral theory” (Russian), M., Nauka, 1978. · Zbl 0408.47039 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.