Acta Mathematica

On the theory of general partial differential operators

Lars Hörmander

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Article information

Source
Acta Math., Volume 94 (1955), 161-248.

Dates
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485892151

Digital Object Identifier
doi:10.1007/BF02392492

Mathematical Reviews number (MathSciNet)
MR76151

Zentralblatt MATH identifier
0067.32201

Rights
1955 © Almqvist & Wiksells Boktryckeri

Citation

Hörmander, Lars. On the theory of general partial differential operators. Acta Math. 94 (1955), 161--248. doi:10.1007/BF02392492. https://projecteuclid.org/euclid.acta/1485892151


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References

  • M. Š. Birman, On the theory of general boundary problems for elliptic differential equations. Doklady Akad. Nauk SSSR (N.S.), 92 (1953), 205–208 (Russian).
  • F. E. Browder, The eigenfunction expansion theorem for the general self-adjoint singular elliptic partial differential operator. I. The analytical foundation. Proc. Nat. Acad. Sci. U.S.A., 40 (1954), 454–459.
  • —, Eigenfunction expansions for singular elliptic operators. II. The Hilbert space argument; parabolic equations on open manifolds. Proc. Nat. Acad. Sci. U.S.A., 40 (1954), 459–463.
  • J. Deny and J. L. Lions, Les espaces du type de Beppo Levi. Ann. Inst. Fourier Grenoble, 5 (1955), 305–370.
  • K. O. Friedrichs, On the differentiability of the solutions of linear elliptic differential equations. Comm. Pure Appl. Math., 6 (1953), 299–326.
  • K. Friedrichs and H. Lewy, Über die Eindeutigkeit und das Abhängigkeitsgebiet der Lösungen beim Anfangsproblem linearer hyperbolischer Differentialgleichungen. Math. Ann., 98 (1928), 192–204.
  • T. Ganelius, On the remainder in a Tauberian theorem. Kungl. Fysiografiska Sällskapets i Lund Förhandlingar, 24, No. 20 (1954).
  • L. Gårding, Linear hyperbolic partial differential equations with constant coefficients. Acta Math., 85 (1951), 1–62.
  • —, Dirichlet's problem for linear elliptic partial differential equations. Math. Scand., 1 (1953), 55–72.
  • —, On the asymptotic distribution of the eigenvalues and eigenfunctions of elliptic differential operators. Math. Scand., 1 (1953), 237–255.
  • L. Gårding, Eigenfunction expansions connected with elliptic differential operators. Comptes rendus du Douzième Congrès des Mathématiciens Scandinaves, Lund, 1953, 44–55.
  • L. Gårding, Applications of the theory of direct integrals of Hilbert spaces to some integral and differential operators. University of Maryland, The Institute for Fluid Dynamics and Applied Mathematics, Lecture Series, No. 11 (1954).
  • L. Gårding, On the asymptotic properties of the spectral function belonging to a self-adjoint semi-bounded extension of an elliptic operator. Kungl. Fysiografiska Sällskapets i Lund förhandlingar, 24, No. 21 (1954).
  • E. Hille, An abstract formulation of Cauchy's problem. Comptes rendus du Douzième Congrès des Mathématiciens Scandinaves, Lund, 1953, 79–89.
  • L. Hörmander, Uniqueness theorems and estimates for normally hyperbolic partial differential equations of the second order. Comptes rendus du Douzième Congrès des Mathématiciens Scandinaves, Lund, 1953, 105–115.
  • F. John, On linear partial differential equations with analytic coefficients. Unique continuation of data. Comm. Pure Appl. Math., 2 (1949), 209–253.
  • M. Krein, Theory of the self-adjoint extensions of semi-bounded hermitian operators and its applications. I. Mat. Sbornik, 20[62] (1947), 431–495 (Russian, English summary).
  • O. Ladyzenskaja, On the closure of the elliptic operator. Doklady Akad. Nauk SSSR (N.S.), 79 (1951), 723–725 (Russian).
  • J. Leray, Hyperbolic Differential Equations. The Institute for Advanced Study, Princeton N.J. (1954).
  • B. Malgrange, Equations aux dérivées partielles à coefficients constants. 1. Solution élémentaire. C. R. Acad. Sci. Paris, 237 (1953), 1620–1622.
  • B. Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution. Thesis, Paris, June 1955.
  • A. Mychkis, Sur les domaines d'unicité pour les solutions des systèmes d'équations linéaires aux dérivées partielles. Mat. Sbornik (N.S.), 19[61] (1946), 489–522 (Russian, French summary).
  • B. v. Sz. Nagy, Spektraldarstellung linearer Transformationen des Hilbertsschen Raumes. Berlin, 1942.
  • J. v. Neumann, Über adjungierte Funktionaloperatoren. Ann. of Math., (2) 33 (1932), 294–310.
  • I. G. Petrowsky, On some problems of the theory of partial differential equations. Amer. Math. Soc., Translation No. 12 (translated from Uspehi Matem. Nauk (N.S.), 1 (1946), No. 3–4 (13–14), 44–70).
  • —, Sur l'analyticité des solutions des systèmes d'équations différentielles. Mat. Sbornik, 5[47] (1939), 3–70 (French, Russian summary).
  • G. de Rham, Solution élémentaire d'équations aux dérivées partielles du second ordre à coefficients constants. Colloque Henri Poincaré (Octobre 1954).
  • L. Schwartz, Théorie des distributions, I–II. Paris, 1950–1951.
  • A. Seidenberg, A new decision method for elementary algebra. Ann. of Math., (2) 60 (1954), 365–374.
  • S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics. Leningrad, 1950 (Russian).
  • S. Täcklind, Sur les classes quasianalytiques des solutions des équations aux dérivées partielles du type parabolique. Nova Acta Soc. Sci. Upsaliensis, (4) 10 (1936), 1–57.
  • A. Tychonov, Théorèmes d'unicité pour l'équation du chaleur. Mat. Sbornik, 42 (1935), 199–216.
  • B. L. van der Waerden, Moderne Algebra, I. Berlin, 1950.
  • M. I. Višik, On general boundary problems for elliptic differential equations. Trudy Moskov. Mat. Obsč., 1 (1952), 187–246 (Russian).
  • A. Zygmund, Trigonometrical Series. Warszawa-Lwow, 1935.