@article{ASNSP_1969_3_23_4_563_0, author = {Kannai, Yakar}, title = {On the asymptotic behavior of resolvent kernels, spectral functions and eigenvalues of semi-elliptic systems}, journal = {Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche}, pages = {563--634}, publisher = {Scuola normale superiore}, volume = {Ser. 3, 23}, number = {4}, year = {1969}, mrnumber = {415092}, zbl = {0193.07301}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1969_3_23_4_563_0/} }
TY - JOUR AU - Kannai, Yakar TI - On the asymptotic behavior of resolvent kernels, spectral functions and eigenvalues of semi-elliptic systems JO - Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche PY - 1969 SP - 563 EP - 634 VL - 23 IS - 4 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_1969_3_23_4_563_0/ LA - en ID - ASNSP_1969_3_23_4_563_0 ER -
%0 Journal Article %A Kannai, Yakar %T On the asymptotic behavior of resolvent kernels, spectral functions and eigenvalues of semi-elliptic systems %J Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche %D 1969 %P 563-634 %V 23 %N 4 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_1969_3_23_4_563_0/ %G en %F ASNSP_1969_3_23_4_563_0
Kannai, Yakar. On the asymptotic behavior of resolvent kernels, spectral functions and eigenvalues of semi-elliptic systems. Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche, Série 3, Tome 23 (1969) no. 4, pp. 563-634. http://www.numdam.org/item/ASNSP_1969_3_23_4_563_0/
[1] On the asymptotic distribution of eigenvalues of differential problems, Seminari dell'Instituto Nazionale di Alta Matematica, 1962-63. Roma: Edizioni Cremonese 1964. 556-573. | MR
,[2] Lectures on Elliptic Boundary Value Problems. Princeton, N. J.: Van No-strand Mathematical Studies, 1965. | MR | Zbl
,[3] On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems. Comm. Pure Appl. Math. 18, 627-663 (1965). | MR | Zbl
,[4] On the asymptotic behavior of spectral functions and resolvent kernels of elliptic operators, Israel J. Math. 5, 1-30 (1967). | MR | Zbl
, and ,[5] Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators, Arch. Rational Mech. Anal. 28, 165-183 (1968). | MR | Zbl
,[6] Uber die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten, Math. Z. 65, 327-344 (1956). | MR | Zbl
,[7] Sul multi-indice degli operatori quasi-ellittici, Boll. Un. Mat. Ital. (3) 19, 289-299 (1964). | MR | Zbl
,[8] Convergence and summability of eigenfunction expansion connected with elliptic differential operators, Med. Lunds. Univ. Math. Sem. 15, 1-63 (1959). | MR | Zbl
,[9] The asymptotic distribution of eigenfunction and eigenvalues for semi-elliptic differential operators, Proc. Nat. Acad. Sci. U. S. A. 43, 270-273 (1957). | MR | Zbl
,[10] Asymptotic distribution of eigenvalues and eigenfunctions for non-local elliptic boundary value problems I, Amer. J. Math. 87, 175-195 (1965). | MR | Zbl
,[11] Proprietes asymptotiques des functions fondamentales des membranes vibrantes, C. R. du 8 ème Congrès des Math. Scand. Stockholm 1934 (Lund 1935), 34-44. | JFM | Zbl
,[12] Sulle proprietà differenziali delle soluzioni delle equazioni quasi-ellittiche relativamente a domini normali, Boll. Un. Mat. Ital. (3) 19, 465-477 (1964). | MR | Zbl
,[13] On a type of eigenvalue problems for certain elliptic differential operators, Math. Scand. 2, 267-285 (1954). | MR | Zbl
,[14] The asymptotic distribution of the eigenvalues and eigenfunctions of a general vibration problem, Kangl. Fysiogr. Sällsk. i Lund Förh. 21, Nr. 11 (1951). This paper appeared also in Med. Lunds. Univ. Mat. Sem. Tome Supplementaire, 19-118 (1952). | MR | Zbl
,[15] On the asymptotic distribution of the eigenvalues and eigenfunctions of elliptic differential operators, Math. Scand. 1, 237-255 (1953). | MR | Zbl
,[16] On the asymptotic properties of the spectral function belonging to a self-adjoint semi-bounded extension of an elliptic differential operator, Kungl. Fysiogr. Sällsk. i Lund Förh, 24, 1-18 (1954). | MR | Zbl
,[17] Equazioni quasi-ellittiche e spazi Lp,θ (Ω, δ), (I), Ann. Mat Pura Appl. (4) 74, 313-354 (1967); (II), Ann. Scuola Norm. Sup. Pisa 21, 353-372 (1967). | Numdam
,[18] Linear Partial Differential Operators, Springer Verlag (1963). | MR | Zbl
[19] On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators. To appear, | MR
,[20] Degenerate elliptic-parabolic equations of second order, Comm. Pure Appl. Math. 20, 797-872 (1967). | MR | Zbl
, and ,[21] Un théorém taubérien avee reste pour la transformée de Stieltjes, C. R. Acad. Sci Paris 255, 2351-2352 (1962). | MR | Zbl
,[22] Asymptotic estimates for spectral functions connected with hypoelliptic differential operators, Arkiv för Mat. 5, 527-540 (1965). | MR | Zbl
,[23] On estimating the solutions of hypoelliptic differential equations near the plane boundary, Math. Scand. 9, 337-251 (1961). | MR | Zbl
,[24] On a theorem by P. Malliavin, Ierael J. Math. 1, 166-168 (1963). | MR | Zbl
,[25] System of partial differential equations in a half-space, Comm. Pure Appl. Math. 17 (1964), 428-484. | MR | Zbl
,[26] Local properties of solution. of quasi-elliptic systems (Russian), Mat. Sb. (N. S.) 59 (101) supplement. 3-52 (1962). | MR | Zbl
,[27] Asymptotic behavior of the Green's function and spectral function of an elliptic operator, to appear. | Zbl
,[28] A priori estimates of solutions to Dirichlet problem for certain hypoelliptic equation, (Russian), Dokl. Akad. Nank. SSSR 179, 783-785 (1968). | MR | Zbl
,[29] spectral function of an elliptic operator, Acta Math. 121 (1968), 198-218. | MR | Zbl