Journal of Lie Theory

no. 1
Cohomological Laplace Transform on Non-convex Cones and Hardy Spaces of ∂-cohomology on Non-convex Tube Domains
Simon Gindikin1; Hideyuki Ishi2
1Dept. of Mathematics, Rutgers University, 110 Frelinghysen Road, Piscataway, NJ 08854-801, U.S.A.
2Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 242-8602, Japan
Journal of Lie Theory, Volume 28 (2018) no. 1, pp. 245-263
We consider a class of non-convex cones $V$ in $\mathbb{R}^n$ which can be presented as (not unique) union of convex cones of some codimension $q$ which we call the index of non-convexity. This class contains non-convex symmetric homogeneous cones studied in D'Atri-Gindikin [{\it Siegel domain realization of pseudo-Hermitian symmetric manifolds}, Geom.\ Dedicata {\bf 46} (1993) 91--125] and Faraut-Gindikin [{\it Pseudo-Hermitian symmetric spaces of tube type}, in: Topics in Geometry, Progr.\ Nonlinear Differential Equations Appl. {\bf 20} (1996) 123--154]. For these cones we consider a construction of dual non-convex cones $V^*$ and corresponding non-convex tubes $T$ and define a cohomological Laplace transform from functions at $V$ to $q$-dimensional cohomology of $T$ using the language of smoothly parameterized \u{C}ech cohomology. We give a construction of Hardy space of $q$-dimensional cohomolgy at $T$.
DOI: 10.5802/jolt.1001
Classification: 32F10, 32C35, 42B30
Keywords: Non-convex cone, Laplace transform, Paley-Wiener Theorem, symmetric cone, cohomology, Hardy norm

Simon Gindikin  1 ; Hideyuki Ishi  2

1 Dept. of Mathematics, Rutgers University, 110 Frelinghysen Road, Piscataway, NJ 08854-801, U.S.A.
2 Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 242-8602, Japan 
Simon Gindikin; Hideyuki Ishi. Cohomological Laplace Transform on Non-convex Cones  and Hardy Spaces of ∂-cohomology on Non-convex Tube Domains. Journal of Lie Theory, Volume 28 (2018) no. 1, pp. 245-263. doi: 10.5802/jolt.1001
@article{JOLT_2018_28_1_a11,
     author = {Simon Gindikin and Hideyuki Ishi},
     title = {Cohomological {Laplace} {Transform} on {Non-convex} {Cones}  and {Hardy} {Spaces} of \ensuremath{\partial}-cohomology on {Non-convex} {Tube} {Domains}},
     journal = {Journal of Lie Theory},
     pages = {245--263},
     year = {2018},
     volume = {28},
     number = {1},
     doi = {10.5802/jolt.1001},
     zbl = {1398.32011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1001/}
}
TY  - JOUR
AU  - Simon Gindikin
AU  - Hideyuki Ishi
TI  - Cohomological Laplace Transform on Non-convex Cones  and Hardy Spaces of ∂-cohomology on Non-convex Tube Domains
JO  - Journal of Lie Theory
PY  - 2018
SP  - 245
EP  - 263
VL  - 28
IS  - 1
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1001/
DO  - 10.5802/jolt.1001
ID  - JOLT_2018_28_1_a11
ER  - 
%0 Journal Article
%A Simon Gindikin
%A Hideyuki Ishi
%T Cohomological Laplace Transform on Non-convex Cones  and Hardy Spaces of ∂-cohomology on Non-convex Tube Domains
%J Journal of Lie Theory
%D 2018
%P 245-263
%V 28
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1001/
%R 10.5802/jolt.1001
%F JOLT_2018_28_1_a11

Cited by Sources: