We show that when is a mean periodic function of tempered growth on the reduced Heisenberg group then the closed translation and rotation invariant subspace generated by contains an elementary spherical function. Using a Paley-Wiener theorem for the Fourier-Weyl transform we formulate a conjecture for arbitrary mean periodic functions.
The aim of this paper is to study mean value operators on the reduced Heisenberg group H/Γ, where H is the Heisenberg group and Γ is the subgroup {(0,2πk): k ∈ Z} of H.
The aim of this paper is to prove certain multiplier theorems for the Hermite series.
It is an interesting open problem to establish Paley-Wiener theorems for general nilpotent Lie groups. The aim of this paper is to prove one such theorem for step two nilpotent Lie groups which is analogous to the Paley-Wiener theorem for the Heisenberg group proved in [4].
Considering functions f on ℝⁿ for which both f and f̂ are bounded by the Gaussian , 0 < a < 1, we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for O(n)-finite functions, thus extending a one-dimensional result of Vemuri.
By a (generalized) Fock space we understand a Hilbert space of entire analytic functions in the complex plane C which are square integrable with respect to a weight of the type e, where Q(z) is a quadratic form such that tr Q > 0. Each such space is in a natural way associated with an (oriented) circle in C. We consider the problem of interpolation between two Fock spaces. If and are the corresponding circles, one is led to consider the pencil of circles generated by and . If H is the...
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