The Bergman projection of 𝐿^{∞} in tubes over cones of real, symmetric, positive-definite matrices

The Bergman projection of $L^ \infty$ in tubes over cones of real, symmetric, positive-definite matrices
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by David Békollé PDF

Trans. Amer. Math. Soc. 296 (1986), 621-639 Request permission

We determine a defining kernel for the Bergman projection of ${L^\infty }$ in tubes over cones of real, symmetric, positive-definite matrices.

References

David Békollé, Le dual de la classe de Bergman $A^{1}$ dans le transformé de Cayley de la boule unité de $\textbf {C}^{n}$, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 9, 377–380 (French, with English summary). MR 703901
David Békollé, Le dual de l’espace des fonctions holomorphes intégrables dans des domaines de Siegel, Ann. Inst. Fourier (Grenoble) 34 (1984), no. 3, 125–154 (French, with English summary). MR 762696, DOI 10.5802/aif.980
David Békollé, The dual of the Bergman space $A^1$ in symmetric Siegel domains of type $\textrm {II}$, Trans. Amer. Math. Soc. 296 (1986), no. 2, 607–619. MR 846599, DOI 10.1090/S0002-9947-1986-0846599-X
R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^{p}$, Representation theorems for Hardy spaces, Astérisque, vol. 77, Soc. Math. France, Paris, 1980, pp. 11–66. MR 604369
S. G. Gindikin, Analysis in homogeneous domains, Uspehi Mat. Nauk 19 (1964), no. 4 (118), 3–92 (Russian). MR 0171941
Stephen Vági, Harmonic analysis on Cartan and Siegel domains, Studies in harmonic analysis (Proc. Conf., DePaul Univ., Chicago, Ill., 1974) MAA Stud. Math., Vol. 13, Math. Assoc. Amer., Washington, D.C., 1976, pp. 257–309. MR 0477178