49
Views
0
CrossRef citations to date
0
Altmetric
Articles

Heat coefficients for magnetic Laplacians on the complex projective space Pn(ℂ)

, &
Pages 993-1020 | Received 10 Feb 2022, Accepted 01 Feb 2023, Published online: 03 Mar 2023

References

  • Davies EB. Heat kernels and spectral theory. Cambridge: Cambridge University Press; 1989. (Cambridge tracts in mathematics; vol. 92).
  • Minakshisundaram S, Pleijel A. Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds. Canad J Math. 1949;1:242–256.
  • Minakshisundaram S. Eigenfunctions on Riemannian manifolds. J Indian Math Soc. 1953;17:158–165.
  • Berger M, Gauduchon P, Mazet E. Le spectre d'une variété riemannienne. Berlin-New York: Springer-Verlag; 1971. (Lecture notes in mathematics; vol. 194).
  • Cahn RS, Wolf JA. Zeta functions and their asymptotic expansions for compact symmetric spaces of rank one. Comm Math Helv. 1976;51:1–21.
  • Bytsenko AA, Williams FL. Asymptotics of the heat kernel on rank-1 locally symmetric spaces. J Phys A: Math Gen. 1999;32:5773–5779.
  • Polterovich I. Combinatorics of the heat trace on spheres. Canad J Math. 2002;54:1086–1099.
  • Cognola G, Vanzo L, Zerbini S. A new algorithm for asymptotic heat kernel expansion for manifolds with boundary. Phys Lett B. 1990;241:381–386.
  • Branson TP, Gilkey PB, Orsted B. Leading terms in the heat invariants. Proc Amer Math Soc. 1990;109:437–450.
  • Awonusika RO. Generalised heat coefficients and associated spectral zeta functions on complex projective spaces Pn(C). Complex Var Elliptic Equ. 2019;65(4):588–620.
  • Hafoud A, Intissar A. Représentation intégrale du noyau de la chaleur sur l'espace projectif complexe. C R Acad Sci Paris Ser 1. 2002;335:871–876.
  • Hafoud A, Intissar A. Reproducing kernels of eigenspaces of a family of magnetic Laplacians on complex projective spaces Pn(C) and their heat kernels. Afr J Math Phys. 2005;2(2):143–153.
  • Besson G, Colbois B, Courtois G. Sur la multiplicité de la première valeur propre de l'opérateur de Schrödinger avec champ magnétique sur la sphère S2. Trans Amer Math Soc. 1998;350(1):331–345.
  • Peetre J, Zhang G. Harmonic analysis on the quantized Riemann sphere. Inter J Math and Math Sci. 1993;16(2):225–243.
  • Demni N, Mouayn Z, Yaqine H. Berezin transforms attached to Landau levels on the complex projective space Pn(C). J Math Phys Geom. 2021;17(4):422–440.
  • Ferapontov EV, Veselov AP. Integrable Schrodinger operators with magnetic fields: factorization method on curved surfaces. J Math Phys. 2001;42:590–607.
  • Dunne GV. Hilbert space for charged particles in perpendicular magnetic field. Ann Phys. 1992;215:233–263.
  • Mouayn Z. Discrete Bargmann transforms attached to Landau levels on the Riemann sphere. Ann Henri Poincaré. 2015;16:641–650.
  • Andrews GE, Askey R, Roy R. Special functions. Cambridge University Press; 1999.
  • Szafraniec FH. The reproducing kernel property and its space: the basics. In: Alpay D, editor. Operator theory. vol. I; Berlin: Springer Reference; 2015. p. 3–30.
  • Koornwinder TH. The addition formula for Jacobi polynomials, II. Math. Centrum Amsterdam AFD. Toegep. Wisk. Report TW 133; 1972.
  • Šapiro RL. Special functions related to representations of the group SU(n), of class I with respect to SU(n−1)(n≥3). Izv Vysš Učeb Zaved Matematika. 1968;4(71):97–107.(Russian).
  • Koornwinder TH. The addition formula for Jacobi polynomials, III. Completion of the proof, Math. Centrum Amsterdam, Report TW 135; 1972.
  • Koornwinder TH. The addition formula for Jacobi polynomials, 2: the Laplace type integral representation and the product formula. Stichting Mathematisch Centrum. Toegepaste Wiskunde TW 133/72; 1972.
  • Hafoud A. Analyse spectrale concrète d'une famille de déformations du Laplacien de Fubini-Study sur l'espace projectif complex Pn(C). In: Thèse de Doctorat Université Mohammed V-Agdal. Faculté des sciences, Rabat, Maroc; 2002.
  • Dijksma A, Koornwinder TH. Spherical harmonics and the product of two Jacobi polynomials. Nederl Akad Wetensch Proc Ser A 74=Indag Math. 1971;33:191–196.
  • Mulholland H. An asymptotic expansion for ∑(2n+1)e−σ(n+1/2)2. Proc Camb Phil Soc. 1928;24:280–289.
  • Prudnikov AP, Brychkov YA, Marichev OI. Elementary functions. Vol. 1. Amsterdam: Gordon and Breach Science Publishers; 1986. (Integrals and series).
  • Rainville ED. Special functions. New York: Macmillan; 1960.
  • Ismail MEH. Classical and quantum orthogonal polynomials in one variable. Cambridge: Cambridge university press; 2005. (Encyclopedia of mathematics and its applications).
  • Zernike F, Brinkman HC. Hypersphãrische Funktionen und die in sphãrischen Bereichen orthogonalen Polynome. Proc Kon Akad V Wet. 1935;38:161–170.Amterdam.
  • Koornwinder TH. The addition formula for Jacobi polynomials II. The Laplace type integral representation and the product formula. Math. Centrum Amsterdam, Report TW 133; 1976.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.