메뉴 건너뛰기




Volumn 199, Issue 6, 2014, Pages 614-628

Hypoelliptic Heat Kernel Over 3-Step Nilpotent Lie Groups

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84902766595     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10958-014-1889-9     Document Type: Article
Times cited : (10)

References (36)
  • 1
    • 62049085213 scopus 로고    scopus 로고
    • The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups
    • A. Agrachev, U. Boscain, J.-P. Gauthier, and F. Rossi, "The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups,"// J. Funct. Anal., 256, 2621-2655 (2009).
    • (2009) J. Funct. Anal. , vol.256 , pp. 2621-2655
    • Agrachev, A.1    Boscain, U.2    Gauthier, J.-P.3    Rossi, F.4
  • 4
    • 0034259983 scopus 로고    scopus 로고
    • Hamilton-Jacobi theory and the heat kernel on Heisenberg groups
    • R. Beals, B. Gaveau, and P. Greiner, "Hamilton-Jacobi theory and the heat kernel on Heisenberg groups,"// J. Math. Pures Appl. (9), 79, No. 7, 633-689 (2000).
    • (2000) J. Math. Pures Appl. , vol.79 , Issue.7 , pp. 633-689
    • Beals, R.1    Gaveau, B.2    Greiner, P.3
  • 5
    • 0002299746 scopus 로고    scopus 로고
    • The tangent space in sub-Riemannian geometry
    • A. Bellaiche and J.-J. Risler (Eds.), Basel: Birkhäuser
    • A. Bellaiche, "The tangent space in sub-Riemannian geometry," In: A. Bellaiche and J.-J. Risler (Eds.), Progr. Math., 144, Sub-Riemannian geometry, 1-78, Birkhäuser, Basel (1996).
    • (1996) Progr. Math., 144, Sub-Riemannian Geometry, 1-78
    • Bellaiche, A.1
  • 9
    • 0005274402 scopus 로고
    • Nonexistence of invariant analytic hypoelliptic differential operators on nilpotent groups of step greater than two
    • M. Christ, "Nonexistence of invariant analytic hypoelliptic differential operators on nilpotent groups of step greater than two," In: Princeton Math., 42, Essays on Fourier analysis in honor of Elias M. Stein, 127-145 (1995).
    • (1995) Essays on Fourier Analysis in Honor of Elias M. Stein , vol.42 , pp. 127-145
    • Christ, M.1
  • 10
    • 0037727573 scopus 로고
    • Heat kernels for class 2 nilpotent groups
    • J. Cygan, "Heat kernels for class 2 nilpotent groups," Studia Math., 64, No. 3, 227-238 (1979).
    • (1979) Studia Math. , vol.64 , Issue.3 , pp. 227-238
    • Cygan, J.1
  • 11
    • 0031537396 scopus 로고    scopus 로고
    • Unfolding the quartic oscillator
    • E. Delabaere and F. Pham, "Unfolding the quartic oscillator," Ann. Physics, 261, No. 2, 180-218 (1997).
    • (1997) Ann. Physics , vol.261 , Issue.2 , pp. 180-218
    • Delabaere, E.1    Pham, F.2
  • 12
    • 0001460125 scopus 로고
    • Sur les représentations unitaires des groupes de Lie algébriques
    • J. Dixmier, "Sur les représentations unitaires des groupes de Lie algébriques," Ann. Inst. Fourier (Grenoble), 7, 315-328 (1957).
    • (1957) Ann. Inst. Fourier (Grenoble) , vol.7 , pp. 315-328
    • Dixmier, J.1
  • 13
    • 0001495481 scopus 로고
    • Sur les représentations unitaries des groupes de Lie nilpotents. III
    • J. Dixmier, "Sur les représentations unitaries des groupes de Lie nilpotents. III," Canad. J. Math. 10, 321-348 (1958).
    • (1958) Canad. J. Math. , vol.10 , pp. 321-348
    • Dixmier, J.1
  • 14
    • 62049084465 scopus 로고
    • Sur les représentations unitaires des groupes de Lie nilpotents. I
    • J. Dixmier, "Sur les représentations unitaires des groupes de Lie nilpotents. I.," Amer. J. Math., 81, 160-170 (1959).
    • (1959) Amer. J. Math. , vol.81 , pp. 160-170
    • Dixmier, J.1
  • 15
    • 84866945959 scopus 로고
    • Analyse harmonique sur les groupes algébriques complexes: Formule de Plancherel (d'aprés M. Andler) et conjecture de M. Vergne
    • M. Duflo, "Analyse harmonique sur les groupes algébriques complexes: formule de Plancherel (d'aprés M. Andler) et conjecture de M. Vergne," Bourbaki Seminar, 1982/83, 279-291.
    • (1982) Bourbaki Seminar , vol.83 , pp. 279-291
    • Duflo, M.1
  • 16
    • 84902829053 scopus 로고    scopus 로고
    • Left-invariant stochastic evolution equations on SE(2) and its applications to contour enhancement and contour completion via invertible orientation scores
    • arxiv: 0711. 0951
    • R. Duits and E. Franken, "Left-invariant stochastic evolution equations on SE(2) and its applications to contour enhancement and contour completion via invertible orientation scores," CASA report, 35, arxiv: 0711. 0951 (2007).
    • (2007) CASA report , pp. 35
    • Duits, R.1    Franken, E.2
  • 18
    • 34250287820 scopus 로고
    • Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents
    • B. Gaveau, "Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents," Acta Math., 139, No. 1-2, 95-153 (1977).
    • (1977) Acta Math. , vol.139 , Issue.1-2 , pp. 95-153
    • Gaveau, B.1
  • 20
    • 0002299742 scopus 로고    scopus 로고
    • Carnot-Caratheodory spaces seen from within
    • A. Bellaiche and J.-J. Risler (Eds.), Basel: Birkhäuser
    • M. Gromov, "Carnot-Caratheodory spaces seen from within," In: A. Bellaiche and J.-J. Risler (Eds.), Progr. Math., 144, Sub-Riemannian geometry, 79-323, Birkhäuser, Basel (1996).
    • (1996) Progr. Math., 144, Sub-Riemannian Geometry, 79-323
    • Gromov, M.1
  • 21
    • 84966224881 scopus 로고
    • Representations of a semisimple Lie group on a Banach space. I
    • Harish-Chandra, "Representations of a semisimple Lie group on a Banach space. I.," Trans. Amer. Math. Soc., 75, 185-243 (1953).
    • (1953) Trans. Amer. Math. Soc. , vol.75 , pp. 185-243
    • Harish-Chandra1
  • 24
    • 15244346736 scopus 로고
    • Hypoelliptic second-order differential equations
    • L. Hörmander, "Hypoelliptic second-order differential equations," Acta Math., 119, 147-171 (1967).
    • (1967) Acta Math. , vol.119 , pp. 147-171
    • Hörmander, L.1
  • 25
    • 0000426179 scopus 로고
    • The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group
    • A. Hulanicki, "The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group," Studia Math., 56, No. 2, 165-173 (1976).
    • (1976) Studia Math. , vol.56 , Issue.2 , pp. 165-173
    • Hulanicki, A.1
  • 28
    • 34250382135 scopus 로고
    • Hypoelliptic differential operators and nilpotent groups
    • L. P. Rothschild and E. M. Stein, "Hypoelliptic differential operators and nilpotent groups," Acta Math., 137, No. 3-4, 247-320 (1976).
    • (1976) Acta Math. , vol.137 , Issue.3-4 , pp. 247-320
    • Rothschild, L.P.1    Stein, E.M.2
  • 29
    • 0742271504 scopus 로고    scopus 로고
    • Symmetries of flat rank-two distributions and sub-Riemannian structures
    • Yu. L. Sachkov, "Symmetries of flat rank-two distributions and sub-Riemannian structures," Trans. Amer. Math. Soc., 356, No. 2, 457-494 (2004).
    • (2004) Trans. Amer. Math. Soc. , vol.356 , Issue.2 , pp. 457-494
    • Sachkov, Y.L.1
  • 30
    • 37849050020 scopus 로고    scopus 로고
    • Complete description of Maxwell strata in the generalized Dido problem
    • Yu. L. Sachkov, "Complete description of Maxwell strata in the generalized Dido problem," Mat. Sb., 197, No. 6, 111-160 (2006).
    • (2006) Mat. Sb. , vol.197 , Issue.6 , pp. 111-160
    • Sachkov, Y.L.1
  • 31
    • 19244379437 scopus 로고    scopus 로고
    • Analytic solutions of the Schrödinger equation for the modified quartic oscillator
    • L. Skála et al., "Analytic solutions of the Schrödinger equation for the modified quartic oscillator," Internat. J. Theoret. Phys., 36, No. 12, 2953-2961 (1997).
    • (1997) Internat. J. Theoret. Phys. , vol.36 , Issue.12 , pp. 2953-2961
    • Skála, L.1
  • 33
    • 84951420422 scopus 로고
    • Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications to the ∂ -Neumann problem
    • F. Tréves, "Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications to the ∂ -Neumann problem," Comm. Partial Differential Equations, 3, 475-642 (1978).
    • (1978) Comm. Partial Differential Equations , vol.3 , pp. 475-642
    • Tréves, F.1
  • 35
    • 0037872644 scopus 로고    scopus 로고
    • The heat kernel and the Riesz transforms on the quaternionic Heisenberg groups
    • F. Zhu, "The heat kernel and the Riesz transforms on the quaternionic Heisenberg groups," Pacific J. Math., 209, No. 1, 175-199 (2003).
    • (2003) Pacific J. Math. , vol.209 , Issue.1 , pp. 175-199
    • Zhu, F.1
  • 36
    • 38149113622 scopus 로고    scopus 로고
    • Heat kernels and Hardy's uncertainty principle on H-type groups
    • F. Zhu and Q. Yang, "Heat kernels and Hardy's uncertainty principle on H-type groups," Acta Math. Sci. Ser. B Engl. Ed., 28, No. 1, 171-178 (2008).
    • (2008) Acta Math. Sci. Ser. B Engl. Ed. , vol.28 , Issue.1 , pp. 171-178
    • Zhu, F.1    Yang, Q.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.