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Spectral synthesis in L2(G) Molitor-Braun, Carine ; ; Pusti, Sanjoy in Colloquium Mathematicum (2015), 138(1), 89104 Detailed reference viewed: 23 (2 UL)Revisiting Beurling's theorem for Dunkl transform Pusti, Sanjoy in Integral Transforms and Special Functions (2015) We prove an analogue of Beurling's theorem in the setting of Dunkl transform, which improves the theorem of Kawazoe-Mejjaoli (\cite{Kawazoe}). Detailed reference viewed: 73 (3 UL)Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications ; ; Pusti, Sanjoy in Advances in Mathematics (2014), 252 A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\l$ is obtained for all $\l \in \fa^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\l$ away from the walls of a Weyl ... [more ▼] A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\l$ is obtained for all $\l \in \fa^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\l$ away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The $L^p$-theory for the hypergeometric Fourier transform is developed for $0<p<2$. In particular, an inversion formula is proved when $1\leq p <2$. [less ▲] Detailed reference viewed: 74 (1 UL)An analogue of Bochner's theorem for Damek-Ricci spaces Pusti, Sanjoy in Journal of Fourier Analysis and Applications (2013), 19(2), 270284 We characterize the image of radial positive measures $\theta$'s on a harmonic $NA$ group $S$ which satisfies $\int_S\phi_0(x)\,d\theta(x)<\infty$ under the spherical transform, where $\phi_0$ is the ... [more ▼] We characterize the image of radial positive measures $\theta$'s on a harmonic $NA$ group $S$ which satisfies $\int_S\phi_0(x)\,d\theta(x)<\infty$ under the spherical transform, where $\phi_0$ is the elementary spherical function. [less ▲] Detailed reference viewed: 103 (6 UL)Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications Pusti, Sanjoy ; ; E-print/Working paper (2012) Detailed reference viewed: 80 (1 UL)AN ANALOGUE OF KREIN’S THEOREM FOR SEMISIMPLE LIE GROUPS Pusti, Sanjoy in Pacific Journal of Mathematics (2011), 254(2), 381395 We give an integral representation of $K$-positive definite functions on a real rank $n$ connected, noncompact, semisimple Lie group with finite centre. Moreover, we characterize the $\lambda$'s for which ... [more ▼] We give an integral representation of $K$-positive definite functions on a real rank $n$ connected, noncompact, semisimple Lie group with finite centre. Moreover, we characterize the $\lambda$'s for which the $\tau$-spherical function $\phi_{\sigma,\lambda}^\tau$ is positive definite for the group $G=\mathrm{Spin}_e(n,1)$ and the complex spin representation $\tau$. [less ▲] Detailed reference viewed: 82 (2 UL)Spectral synthesis in $L^2(G)$ ; Molitor-Braun, Carine ; Pusti, Sanjoy in Preprint (n.d.) For locally compact, second countable, type I groups $G$, we characterize all closed (two-sided) translation invariant subspaces of $L^2(G)$. We establish a similar result for $K$-biinvariant $L^2 ... [more ▼] For locally compact, second countable, type I groups $G$, we characterize all closed (two-sided) translation invariant subspaces of $L^2(G)$. We establish a similar result for $K$-biinvariant $L^2$-functions ($K$ a fixed maximal compact subgroup) in the context of semisimple Lie groups. [less ▲] Detailed reference viewed: 117 (3 UL) |
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