@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},
year = {1969},
publisher = {Scuola normale superiore},
volume = {Ser. 3, 23},
number = {4},
mrnumber = {415092},
zbl = {0193.07301},
language = {en},
url = {https://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 - https://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 https://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. https://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. | Zbl | MR
[3] , On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems. Comm. Pure Appl. Math. 18, 627-663 (1965). | Zbl | MR
[4] , and , On the asymptotic behavior of spectral functions and resolvent kernels of elliptic operators, Israel J. Math. 5, 1-30 (1967). | Zbl | MR
[5] , Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators, Arch. Rational Mech. Anal. 28, 165-183 (1968). | Zbl | MR
[6] , Uber die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten, Math. Z. 65, 327-344 (1956). | Zbl | MR
[7] , Sul multi-indice degli operatori quasi-ellittici, Boll. Un. Mat. Ital. (3) 19, 289-299 (1964). | Zbl | MR
[8] , Convergence and summability of eigenfunction expansion connected with elliptic differential operators, Med. Lunds. Univ. Math. Sem. 15, 1-63 (1959). | Zbl | MR
[9] , The asymptotic distribution of eigenfunction and eigenvalues for semi-elliptic differential operators, Proc. Nat. Acad. Sci. U. S. A. 43, 270-273 (1957). | Zbl | MR
[10] , Asymptotic distribution of eigenvalues and eigenfunctions for non-local elliptic boundary value problems I, Amer. J. Math. 87, 175-195 (1965). | Zbl | MR
[11] , Proprietes asymptotiques des functions fondamentales des membranes vibrantes, C. R. du 8 ème Congrès des Math. Scand. Stockholm 1934 (Lund 1935), 34-44. | Zbl | JFM
[12] , Sulle proprietà differenziali delle soluzioni delle equazioni quasi-ellittiche relativamente a domini normali, Boll. Un. Mat. Ital. (3) 19, 465-477 (1964). | Zbl | MR
[13] , On a type of eigenvalue problems for certain elliptic differential operators, Math. Scand. 2, 267-285 (1954). | Zbl | MR
[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). | Zbl | MR
[15] , On the asymptotic distribution of the eigenvalues and eigenfunctions of elliptic differential operators, Math. Scand. 1, 237-255 (1953). | Zbl | MR
[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). | Zbl | MR
[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). | Zbl | MR
[19] , On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators. To appear, | MR
[20] , and , Degenerate elliptic-parabolic equations of second order, Comm. Pure Appl. Math. 20, 797-872 (1967). | Zbl | MR
[21] , Un théorém taubérien avee reste pour la transformée de Stieltjes, C. R. Acad. Sci Paris 255, 2351-2352 (1962). | Zbl | MR
[22] , Asymptotic estimates for spectral functions connected with hypoelliptic differential operators, Arkiv för Mat. 5, 527-540 (1965). | Zbl | MR
[23] , On estimating the solutions of hypoelliptic differential equations near the plane boundary, Math. Scand. 9, 337-251 (1961). | Zbl | MR
[24] , On a theorem by P. Malliavin, Ierael J. Math. 1, 166-168 (1963). | Zbl | MR
[25] , System of partial differential equations in a half-space, Comm. Pure Appl. Math. 17 (1964), 428-484. | Zbl | MR
[26] , Local properties of solution. of quasi-elliptic systems (Russian), Mat. Sb. (N. S.) 59 (101) supplement. 3-52 (1962). | Zbl | MR
[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). | Zbl | MR
[29] spectral function of an elliptic operator, Acta Math. 121 (1968), 198-218. | Zbl | MR





