Geodesic
On Isomorphism Between Certain Group Algebras on the Heisenberg Group
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 2, pp. 150-164 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $I\!\!H_n$ denote the $(2n+1)$-dimensional Heisenberg group and let $K$ be a compact subgroup of $Aut(I\!\!H_n)$, the group of automorphisms of $I\!\!H_n$. We prove that the algebra of radial functions on $I\!\!H_n$ and the algebra of spherical functions arising from the Gelfand pairs of the form $(K, I\!\!H_n)$ are algebraically isomorphic. 
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M. E. Egwe; U. N. Bassey. On Isomorphism Between Certain Group Algebras on the Heisenberg Group. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 2, pp. 150-164. http://geodesic.mathdoc.fr/item/JMAG_2013_9_2_a1/

[1] B. Krotz, S. Thangavelu, Y. Xu, The Heat Kernel Transform for the Heisenberg Group, 2005, arXiv: math.CA/0401243v2 | MR

[2] A. Sikora, J. Zienkiewicz, “A Note on Heat Kernel on the Heisenberg Group”, Bull. Austral Math. Soc., 65:1 (2002), 116–120 | DOI | MR

[3] M. Cowling, S. Giulini, G. Mauceri, “Weak $(1,1)$ Estimates for Heat Kernel Maximal Functions on Lie Groups”, Trans. Amer. Math. Soc., 323 (1991), 637–649 | MR | Zbl

[4] S. Thangavelu, “Spherical Means on the Heisenberg Group and a Restriction Theorem for the Symplectic Fourier Transform”, Revista Math. Iberoamericana, 7:2 (1991), 135–165 | DOI | MR

[5] J. Ludwig, “Hull-Minimal Ideals in the Schwartz Algebra of the Heisenberg Group”, Stud. Math., 130:1 (1998), 77–98 | MR | Zbl

[6] G. B. Folland, E. M. Stein, “Estimates for the $\bar{\partial}_b$ Complex and Analysis on the Heisenberg Group”, Commun. Pure and Appl. Math., XXVII (1974), 429–522 | DOI | MR | Zbl

[7] G. Mauceri, “Zonal Multipliers On the Heisenberg Group”, Pacific J. Math., 95 (1981), 143–169 | DOI | MR

[8] S. Lang, $SL(2,I\!\!R)$, Addison-Wesley, Reading, MA, 1975 | MR | Zbl

[9] R. Gangolli, “Spherical Functions on Semisimple Lie Groups”, Symmetric Spaces, eds. W. Boothy, G. Weiss, Marcel Dekker, Inc., New York, 1972 | MR

[10] B. Astengo, D. B. Blasio, F. Ricci, “Gelfand Pairs on the Heisenberg Group and Schwartz Functions”, J. Funct. Anal., 256:5 (2009), 1565–1587 | DOI | MR | Zbl

[11] C. Benson, J. Jenkins, G. Ratcliff, “Bounded $K$-Spherical Functions on the Heisenberg Groups”, J. Funct. Anal., 105 (1992), 409–443 | DOI | MR | Zbl

[12] G. E. Andrews, R. Askey, R. Roy, Special Functions, Encyclopedia of Math. and its Appl., Cambridge Univ. Press, UK, Cambridge, 2000 | MR | Zbl

[13] S. Helgason, Groups and Geometric Analysis: Integral Geometry, Differential Operators and Spherical Functions, Acad. Press Inc., New York, 1984 | MR | Zbl

[14] E. M. Stein, G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, London, 1971 | MR

[15] G. Szego, Orthogonal Polynomials, AMS Colloq. Publ., XXIII, AMS, Providence, RI, 1939 | Zbl

[16] S. Bochner, K. Chandrasekharan, Fourier Transforms, Princeton Univ. Press, London, 1949 | MR

[17] N. Leptin, “On Group Algebras of Nilpotent Groups”, Stud. Math., 47 (1973), 37–49 | MR | Zbl

[18] A. Hulanicki, F. Ricci, “A Tauberian Theorem and Tangential Convergence of Bounded Harmonic Functions on Balls in ${I\!\!\!\!C}^n$”, Inv. Math., 62 (1980), 325–331 | DOI | MR | Zbl

[19] N. Lyall, “The Heisenberg Group Fourier Transform”, Trans. Amer. Math. Soc., 359 (2007), 4467–4488 | DOI | MR | Zbl

[20] M. E. Taylor, Noncommutative Harmonic Analysis, AMS, Providence, RI, USA, 1986 | MR