Kotake, Takeshi; Narasimhan, Mudumbai S. Regularity theorems for fractional powers of a linear elliptic operator. (English) Zbl 0104.32503 Bull. Soc. Math. Fr. 90, 449-471 (1962). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 53 Documents Keywords:partial differential equations × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] BERGENDAL (G.) . - On spectral functions belonging to an elliptic differential operator with variable coefficients , Math. Scand., t. 5, 1957 , p. 241-254. MR 20 #1830 | Zbl 0080.30701 · Zbl 0080.30701 [2] BERGENDAL (G.) . - Convergence and summability of eigenfunction expansions connected with elliptic differential operators , Medd. Lunds Univ. Mat. Sem., t. 15, 1959 . MR 21 #4287 | Zbl 0093.06901 · Zbl 0093.06901 [3] BOCHNER (S.) . - Zeta functions and Green’s functions for linear partial differential operators of elliptic type with constant coefficients , Annals of Math., Series 2, t. 57, 1953 , p. 32-56. MR 14,986d | Zbl 0050.08001 · Zbl 0050.08001 · doi:10.2307/1969725 [4] BROWDER (Felix E.) . - The eigenfunction expansion theorem for the general self-adjoint singular elliptic partial differential operator, I : The analytic foundation , Proc. Nat. Acad. Sc. U. S. A., t. 40, 1954 , p. 454-459. Zbl 0055.34302 · Zbl 0055.34302 [5] BROWDER (Felix E.) . - Eigenfunction expansions for singular elliptic operators, II : The Hilbert space argument, parabolic equations on open manifolds , Proc. Nat. Acad. Sc. U. S. A., t. 40, 1954 , p. 459-463. MR 16,134d | Zbl 0055.34302 · Zbl 0055.34302 [6] EIDELMAN (S. D.) . - On fundamental solutions of parabolic systems [in russian] , Mat. Sbornik, t. 38, (80), 1956 , p. 51-92. MR 17,857a [7] FRIEDRICHS (K. O.) . - On the differentiability of the solutions of the linear elliptic differential equations , Comm. pure and appl. Math., t. 6, 1953 , p. 299-326. MR 15,430c | Zbl 0051.32703 · Zbl 0051.32703 · doi:10.1002/cpa.3160060301 [8] GÅRDING (L.) . - On the asymptotic properties of the spectral function belonging to a self-adjoint semi-bounded extension of an elliptic differential operator , Kungl. Fysiogr. Sallsk. Lund Forh., t. 24, 1954 , n^\circ 21, p. 1-18. MR 17,158d | Zbl 0058.08802 · Zbl 0058.08802 [9] GÅRDING (L.) . - Dirichlet’s problem for linear elliptic partial differential equations , Math. Scand., t. 1, 1953 , p. 55-72. MR 16,366a | Zbl 0053.39101 · Zbl 0053.39101 [10] KOTAKE (T.) and NARASIMHAN (M. S.) . - Sur la régularité de certains noyaux associés à un opérateur elliptique , C. R. Acad. Sc. Paris, t. 252, 1961 , p. 1549-1550. MR 23 #A3370 | Zbl 0097.30502 · Zbl 0097.30502 [11] LIONS (J.-L.) . - Lectures on elliptic partial differential equations . - Bombay, Tata Institute of fundamental Research, 1957 . Zbl 0253.35001 · Zbl 0253.35001 [12] MINAKSHISUNDARAM (S.) . - A generalization of Epstein zeta functions , Canadian J. Math., t. 1, 1947 , p. 320-327. MR 11,357c | Zbl 0034.05103 · Zbl 0034.05103 · doi:10.4153/CJM-1949-029-3 [13] MORREY Jr (C. B.) and NIRENBERG (L) . - On the analyticity of the solutions of linear elliptic systems of partial differential equations , Comm. pure and appl. Math., t. 10, 1957 , p. 271-290. MR 19,654b | Zbl 0082.09402 · Zbl 0082.09402 · doi:10.1002/cpa.3160100204 [14] NELSON (Edward) . - Analytic vectors , Annals of Math., t. 70, 1959 , p. 572-615. MR 21 #5901 | Zbl 0091.10704 · Zbl 0091.10704 · doi:10.2307/1970331 [15] NIRENBERG (Louis) . - Remarks on strongly elliptic partial differential equations , Comm. pure and appl. Math., t. 8, 1955 , p. 648-674. MR 17,742d | Zbl 0067.07602 · Zbl 0067.07602 · doi:10.1002/cpa.3160080414 [16] RIESZ (F.) and NAGY (Béla, Sz) . - Leçons d’analyse fonctionnelle , 3e éd. - Paris, Gauthier-Villars ; Budapest, Akademiai Kiodo, 1955 . Zbl 0064.35404 · Zbl 0064.35404 [17] SCHWARTZ (Laurent) . - Théorie des distributions , Tome 1, 2e éd. - Paris, Hermann, 1957 (Act. scient. et ind., 1091-1245 ; Publ. Inst. Math. Univ. Strasbourg, 9). Zbl 0078.11003 · Zbl 0078.11003 [18] SCHWARTZ (Laurent) . - Théorie des distributions , Tome 2. - Paris, Hermann, 1951 (Act. scient. et ind., 1122 ; Publ. Inst. Math. Univ. Strasbourg, 10). Zbl 0042.11405 · Zbl 0042.11405 [19] SCHWARTZ (Laurent) . - Théorie des noyaux , Proc. Intern. Congr. Math. [11, 1950 . Cambridge (Mass.)] ; p. 220-230. - Providence, American mathematical Society , 1952 . Zbl 0048.35102 · Zbl 0048.35102 [20] STONE (Marshall H.) . - Linear transformations in Hilbert space and their applications to analysis . - New York, American mathematical Society, 1932 (American mathematical Society, Colloquim Publicalions, 15). Zbl 0005.40003 | JFM 58.0420.02 · Zbl 0005.40003 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.