Geodesic
Lacunas for hyperbolic differential operators with constant coefficients. I
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 26 (1971) no. 2 Cet article a éte moissonné depuis la source Math-Net.Ru

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M. F. Atiyah; R. Bott; L. Gårding. Lacunas for hyperbolic differential operators with constant coefficients. I. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 26 (1971) no. 2. http://geodesic.mathdoc.fr/item/RM_1971_26_2_a9/

[1] M. F. Atiyah, W. D. V. Hodge, “Integrals of the second kind of an algebraic variety”, Ann. of Math., 62 (1955), 56–91 | DOI | MR | Zbl

[2] J. Bazer, D. H. Y. Yen, “The Riemann matrix of $(2+1)$-dimensional symmetric-hyperbolic systems”, Comm. Pure Appl. Math., 20 (1967), 329–363 | MR | Zbl

[3] J. Bazer, D. H. Y. Yen, Lacunas of the Riemann matrix of symmetric-hyperbolic systems, in two space variables, Preprint, Courant Inst., New York Univ., 1969 | MR

[4] V. A. Borovikov, “Fundamentalnye resheniya lineinykh uravnenii v chastnykh proizvodnykh s postoyannymi koeffitsientami”, Tr. Mosk. matem. o-va, 8, 1959, 199–257 | MR

[5] V. A. Borovikov, “Nekotorye dostatochnye usloviya otsutstviya lakun”, Matem. sb., 55(97) (1961), 237–254 | MR | Zbl

[6] R. Burridge, “Lacunas in two-dimensional wave propagation”, Proc. Cambridge Phil. Soc., 63 (1967), 819–825 | DOI | MR | Zbl

[7] L. Gårding, “The solution of Cauchy's problem for two totally hyperbolic linear differential equations by means of Riesz integrals”, Ann. of Math., 48 (1947), 785–826 ; Errata, Ann. of Math., 52 (1950), 506–507 | DOI | MR | DOI

[8] L. Gårding, “Linear hyperbolic partial differential equations with constant coefficients”, Acta Math., 85 (1950), 1–62 | MR

[9] L. Gårding, “An inequality for hyperbolic polynomials”, J. Math. Mech., 8 (1959), 957–966 | MR

[10] L. Gårding, “Transformation de Fourier des distributions homogènes”, Bull. Soc. Math. France, 89 (1961), 381–428 | MR

[11] L. Gårding, “The theory of lacunas”, Battelle Seattle 1968 Rencontres, Springer, 1969, 13–21 | MR

[12] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii, vyp. 1, M., 1958 | Zbl

[13] S. G. Gindikin, “Zadacha Koshi dlya silno odnorodnykh differentsialnykh operatorov”, Tr. Mosk. matem. o-va, 16, 1967, 181–208 | MR | Zbl

[14] A. Grothendieck, “On the de Rham cohomology of algebraic varieties”, Publ. IHES, 29 (1966), 351–359 | MR | Zbl

[15] J. Hadamard, Le problème de Cauchy et les équations aux dérivées partielles linéaires hyperboliques, Paris, 1932 | Zbl

[16] G. Herglotz, “Über die Integration linearer partieller Differentialgleichungen. I (Anwendung Abelscher Integrale)”, Leipzig. Ber. Sächs, Akad. Wiss., Math. Phys. Kl., 78 (1926), 93–126 ; “II; III (Anwendung Fourierscher Integrale)”, Leipzig. Ber. Sächs, Akad. Wiss., Math. Phys. Kl., 80 (1928), 6–114 | Zbl

[17] L. Khërmander, Lineinye differentsialnye operatory s chastnymi proizvodnymi, «Mir», M., 1965 | MR

[18] L. Hörmander, “On the singularities of solutions of partial differential equations”, Intern. Conf. of Funct. Analysis and Related Topics, Tokyo, 1969

[19] Zh. Lere, Obobschennoe preobrazovanie Laplasa, «Mir», M., 1960

[20] J. Leray, Hyperbolic differential equations, The Inst. for Advanced Study, Princeton, N. J., 1952 | MR

[21] D. Ludwig, “Singularities of superpositions of distributions”, Pacific J. Math., 15 (1965), 215–239 | MR | Zbl

[22] W. Nuij, “A note on hyperbolic polynomials”, Math. Scand., 23 (1968), 69–72 | MR | Zbl

[23] I. G. Petrovskii, “On the diffusion of waves and the lacunas for hyperbolic equations”, Matem. sb., 17 (59) (1945), 289–370 | MR

[24] M. Riesz, “L'intégrale de Riemann - Liouviile et le problème de Cauchy”, Acta Math., 81 (1949), 1–223 | DOI | MR | Zbl

[25] L. Schwartz, Théorie des distributions, t. I–II, Paris, 1950–1951

[26] K. L. Stellmacher, “Eine Klasse huygenscher Differentialgleichungen und ihre Integration”, Math. Ann., 130 (1955), 219–233 | DOI | MR | Zbl

[27] L. Svensson, “Necessary and sufficient conditions for the hyperbolicity of polynomials with hyperbolic principal part”, Ark. Math., 8 (1970) | DOI | MR | Zbl

[28] B. R. Vainberg, S. G. Gindikin, “Ob usilennom printsipe Gyuigensa dlya odnogo klassa differentsialnykh operatorov s postoyannymi koeffitsientami”, Tr. Mosk. matem. o-va, 16, 1967, 151–180 | MR | Zbl

[29] H. Weitzner, “Green's function for two-dimensional magnetohydrodynamic waves. I; II”, Phys. Fluids, 4 (1961), 1238–1245 ; 1246–1250 | DOI | MR | DOI