메뉴 건너뛰기




Volumn 352, Issue 8, 2000, Pages 3743-3776

The problem of lacunas and analysis on root systems

Author keywords

Coxeter groups; Dunkl operators; Fundamental solution; Huygens' principle; Hyperbolic linear differential operators; Lacuna

Indexed keywords


EID: 23044517948     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (12)

References (67)
  • 1
    • 84980085922 scopus 로고
    • Some hints on Huygens' principle and Hadamard's conjecture
    • MR 18:487d
    • L. Asgeirsson, Some hints on Huygens' principle and Hadamard's conjecture, Comm. Pure Appl. Math., 9 (1956), 307-326. MR 18:487d
    • (1956) Comm. Pure Appl. Math. , vol.9 , pp. 307-326
    • Asgeirsson, L.1
  • 2
    • 0000311887 scopus 로고
    • Lacunas for hyperbolic differential operators with constant coefficients I
    • MR 5T:10252a
    • M.F. Atiyah, R. Bott, and L. Carding, Lacunas for hyperbolic differential operators with constant coefficients I, Acta Math., 124 (1970), 109-189. MR 5T:10252a
    • (1970) Acta Math. , vol.124 , pp. 109-189
    • Atiyah, M.F.1    Bott, R.2    Carding, L.3
  • 3
    • 0001565106 scopus 로고
    • Lacunas for hyperbolic differential operators with constant coefficients II
    • MR 57:10252b
    • M.F. Atiyah, R. Bott, and L. Carding, Lacunas for hyperbolic differential operators with constant coefficients II, Acta Math., 131 (1973), 145-206. MR 57:10252b
    • (1973) Acta Math. , vol.131 , pp. 145-206
    • Atiyah, M.F.1    Bott, R.2    Carding, L.3
  • 4
    • 0039937348 scopus 로고    scopus 로고
    • Lacunae of hyperbolic Riesz kernels and commutative rings of partial differential operators
    • MR 98k:58103
    • Yu.Yu. Bercst, Lacunae of hyperbolic Riesz kernels and commutative rings of partial differential operators, Lett. Math. Phys. 41 (1997), 227-235. MR 98k:58103
    • (1997) Lett. Math. Phys. , vol.41 , pp. 227-235
    • Bercst, Y.Y.1
  • 5
    • 0031498011 scopus 로고    scopus 로고
    • Solution of a restricted Hadamard problem on Minkowski spaces
    • MR 99c:35135
    • Yu.Yu. Bcrest, Solution of a restricted Hadamard problem on Minkowski spaces, Comm. Pure Appl. Math., 50 (1997), 1019-1052. MR 99c:35135
    • (1997) Comm. Pure Appl. Math. , vol.50 , pp. 1019-1052
    • Bcrest, Y.Y.1
  • 7
    • 21844496103 scopus 로고
    • Fundamental solutions for partial differential operators with reflection group invariance
    • MR 96c:35005
    • Yu.Yu. Berest, and Yu.A. Molchanov, Fundamental solutions for partial differential operators with reflection group invariance, J. Math. Phys. 36(8) (1995), 4324-4339. MR 96c:35005
    • (1995) J. Math. Phys. , vol.36 , Issue.8 , pp. 4324-4339
    • Berest, Y.Y.1    Molchanov, Y.A.2
  • 8
    • 84956224104 scopus 로고
    • Huygens' principle and Coxeter groups
    • MR 94i:35110
    • Yu.Yu. Bercst, and A.P. Veselov, Huygens' principle and Coxeter groups, Russian Math. Surveys, 48(2) (1993), 183-184. MR 94i:35110
    • (1993) Russian Math. Surveys , vol.48 , Issue.2 , pp. 183-184
    • Bercst, Y.Y.1    Veselov, A.P.2
  • 9
    • 0009109633 scopus 로고
    • Hadamard's problem and Coxeter groups: New examples of Huygens' equations
    • MR 95h:58131
    • Yu.Yu. Berest, and A.P. Veselov, Hadamard's problem and Coxeter groups: new examples of Huygens' equations, Funct. Anal. Appl., 28 (1994), 3-12. MR 95h:58131
    • (1994) Funct. Anal. Appl. , vol.28 , pp. 3-12
    • Berest, Y.Y.1    Veselov, A.P.2
  • 10
    • 84957337849 scopus 로고
    • Huygens' principle and integrability
    • MR 96a:35003
    • Yu.Yu. Berest, and A.P. Veselov, Huygens' principle and integrability, Russian Math. Surveys, 49(6) (1994), 5-77. MR 96a:35003
    • (1994) Russian Math. Surveys , vol.49 , Issue.6 , pp. 5-77
    • Berest, Y.Y.1    Veselov, A.P.2
  • 11
    • 33646879463 scopus 로고
    • Some sufficient conditions for the absence of lacunas
    • (Russian) MR 25:5284
    • V.A. Borovikov, Some sufficient conditions for the absence of lacunas, Mat. Sbornik, 55 (3) (1961), 237-254. (Russian) MR 25:5284
    • (1961) Mat. Sbornik , vol.55 , Issue.3 , pp. 237-254
    • Borovikov, V.A.1
  • 12
    • 84908253040 scopus 로고
    • Lacunas and transmissions in Seminar on Singularities of Solutions of Linear Partial Differential Equations
    • Princeton Univ. Press, Princeton, MR 80k:58092
    • L. Boutct de Monvcl, Lacunas and transmissions in Seminar on Singularities of Solutions of Linear Partial Differential Equations, Ann. of Math. Stud. 91, Princeton Univ. Press, Princeton, 1978, pp. 209-218. MR 80k:58092
    • (1978) Ann. of Math. Stud. , vol.91 , pp. 209-218
    • De Boutct Monvcl, L.1
  • 16
    • 33646872510 scopus 로고
    • Hypergeometric partial differential equations
    • T.W. Chaundy, Hypergeometric partial differential equations, Quart. J. Math., Oxford Ser. 6 (1935), 288-303;
    • (1935) Quart. J. Math., Oxford Ser. , vol.6 , pp. 288-303
    • Chaundy, T.W.1
  • 23
    • 84948867463 scopus 로고
    • Singularities, supports and lacunas, in Advances in Microlocal Analysis
    • Reidel, Dordrecht-Boston, MR 87j:35003
    • G.F.D. Duff, Singularities, supports and lacunas, in Advances in Microlocal Analysis, NATO Adv. Sei. Inst. Ser. C: JNlath. Phys. Sei., 168, Reidel, Dordrecht-Boston, 1986, pp. 73-133. MR 87j:35003
    • (1986) NATO Adv. Sei. Inst. Ser. C: JNlath. Phys. Sei. , vol.168 , pp. 73-133
    • Duff, G.F.D.1
  • 29
    • 0011686240 scopus 로고    scopus 로고
    • "Selected Works", Part I
    • Gordon and Breach Publ., Amsterdam
    • English transi, in: I. G. Petrovsky, "Selected Works", Part I, Classics of Soviet Mathematics 5, Gordon and Breach Publ., Amsterdam, 1996, pp. 485-495.
    • (1996) Classics of Soviet Mathematics , vol.5 , pp. 485-495
    • Petrovsky, I.G.1
  • 30
    • 33646867930 scopus 로고
    • The Cauchy problem for differential operators decomposing into wave factors
    • MR 37:585
    • S.A. Gal'pern, and V.E. Kondrashov, The Cauchy problem for differential operators decomposing into wave factors, Trans. Moscow Math. Soc., 16 (1967), 117-145. MR 37:585
    • (1967) Trans. Moscow Math. Soc. , vol.16 , pp. 117-145
    • Gal'Pern, S.A.1    Kondrashov, V.E.2
  • 31
    • 0001541026 scopus 로고
    • The solution of Cauchy's problem for two totally hyperbolic linear differential equations by means of Riesz integrals
    • MR 9:240a
    • L. Carding, The solution of Cauchy's problem for two totally hyperbolic linear differential equations by means of Riesz integrals, Ann. Math., 48 (1947), 785-826. MR 9:240a
    • (1947) Ann. Math. , vol.48 , pp. 785-826
    • Carding, L.1
  • 32
    • 34250597684 scopus 로고
    • Linear hyperbolic partial differential equations with constant coefficients
    • MR 12:831g
    • L. Carding, Linear hyperbolic partial differential equations with constant coefficients, Acta Math., 85 (1950), 1-62. MR 12:831g
    • (1950) Acta Math. , vol.85 , pp. 1-62
    • Carding, L.1
  • 37
    • 0039722396 scopus 로고
    • Tube Domains and the Cauchy Problem
    • Amer. Math. Soc., Providence, RI, MR 94d:35028
    • S.G. Gindikin, Tube Domains and the Cauchy Problem, 111, Amer. Math. Soc., Providence, RI, 1992. MR 94d:35028
    • (1992) 3ETransi. Math. Monographs , vol.111
    • Gindikin, S.G.1
  • 45
    • 0003668851 scopus 로고
    • I-IV, Springer-Verlag, Berlin, MR 85g:35002a, MR 85g:35002b; MR 87d:35002a; MR 87d:35002b
    • L. Hörmander, The Analysis of Linear Partial Differential Operators, I-IV, Springer-Verlag, Berlin, 1983-85. MR 85g:35002a, MR 85g:35002b; MR 87d:35002a; MR 87d:35002b
    • (1983) The Analysis of Linear Partial Differential Operators
    • Hörmander, L.1
  • 53
    • 0007456353 scopus 로고
    • Quantum integrable systems related to Lie algebras
    • MR 84k:81007
    • M.A. Olshanetsky, arid "A.M. Perelomov, Quantum integrable systems related to Lie algebras, Phys. Reps., 94 (1983), 313-404. MR 84k:81007
    • (1983) Phys. Reps. , vol.94 , pp. 313-404
    • Olshanetsky, M.A.1    Perelomov, A.M.2
  • 61
    • 0040699330 scopus 로고
    • A strengthened Huygens' principle for a class of differential operators with constant coefficients
    • MR 37:3176
    • B.R. Vainberg, S.G. Gindikin, A strengthened Huygens' principle for a class of differential operators with constant coefficients, Trans. Moscow Math. Soc., 16 (1967), 163-196. MR 37:3176
    • (1967) Trans. Moscow Math. Soc. , vol.16 , pp. 163-196
    • Vainberg, B.R.1    Gindikin, S.G.2
  • 62
    • 33646884682 scopus 로고
    • Sharpness and local Petrovsky condition for strictly hyperbolic operators with constant coefficients
    • V.A. Vassiliev, Sharpness and local Petrovsky condition for strictly hyperbolic operators with constant coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 50(2) (1986), 243-284;
    • (1986) Izv. Akad. Nauk SSSR Ser. Mat. , vol.50 , Issue.2 , pp. 243-284
    • Vassiliev, V.A.1
  • 63
    • 0012230942 scopus 로고
    • MR 88a:58193
    • English transi, Math. USSR Izv. 28 (1987), 233-273. MR 88a:58193
    • (1987) Math. USSR Izv. , vol.28 , pp. 233-273
  • 64
    • 0007464689 scopus 로고
    • Ramified Integrals, Singularities and Lacunas
    • Kluwcr Acad. Publ., MR 96h:32052
    • V.A. Vassiliev, Ramified Integrals, Singularities and Lacunas, Mathematics and its Appl., 315, Kluwcr Acad. Publ., 1995. MR 96h:32052
    • (1995) Mathematics and Its Appl. , vol.315
    • Vassiliev, V.A.1
  • 67
    • 33646881582 scopus 로고    scopus 로고
    • MR 97e:58122
    • English transi, in Russian Math. Surveys 57 (1996), no. 3. MR 97e:58122
    • (1996) Russian Math. Surveys , vol.57 , Issue.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.