Regularity theorems for fractional powers of a linear elliptic operator
Bulletin de la Société Mathématique de France, Tome 90 (1962), p. 449-471
@article{BSMF_1962__90__449_0,
     author = {Kotake, Takeshi and Narasimhan, Mudumbai},
     title = {Regularity theorems for fractional powers of a linear elliptic operator},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {90},
     year = {1962},
     pages = {449-471},
     doi = {10.24033/bsmf.1584},
     zbl = {0104.32503},
     mrnumber = {26 \#6819},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_1962__90__449_0}
}
Kotake, Takeshi; Narasimhan, Mudumbai S. Regularity theorems for fractional powers of a linear elliptic operator. Bulletin de la Société Mathématique de France, Tome 90 (1962) pp. 449-471. doi : 10.24033/bsmf.1584. https://www.numdam.org/item/BSMF_1962__90__449_0/

[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

[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

[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

[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

[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

[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

[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° 21, p. 1-18. | MR 17,158d | 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

[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

[11] Lions (J.-L.). - Lectures on elliptic partial differential equations. - Bombay, Tata Institute of fundamental Research, 1957. | 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

[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

[14] Nelson (Edward). - Analytic vectors, Annals of Math., t. 70, 1959, p. 572-615. | MR 21 #5901 | Zbl 0091.10704

[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

[16] Riesz (F.) and Nagy (Béla, Sz). - Leçons d'analyse fonctionnelle, 3e éd. - Paris, Gauthier-Villars ; Budapest, Akademiai Kiodo, 1955. | 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

[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

[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

[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). | JFM 58.0420.02 | Zbl 0005.40003