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Spectral synthesis in L2(G) Molitor, Carine ; ; Pusti, Sanjoy in Colloquium Mathematicum (2015), 138(1), 89104 Detailed reference viewed: 15 (0 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: 60 (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: 84 (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: 57 (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: 62 (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: 63 (0 UL)Revisiting Beurling's theorem for Dunkl transform ; Pusti, Sanjoy in Preprint (n.d.) 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: 64 (0 UL) |
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