In this paper we consider the question of sampling for spaces entire functions exponential type in several variables. The novelty resides growth condition impose, that is, their restriction to a hypersurface is square integrable with respect natural measure. boundary $b\mathcal U$ Siegel upper half-space $\mathcal and it fundamental can be identified Heisenberg group $\mathbb H_n$. We C^{n+1}$ ...

We propose a nonparametric estimator of the expected discounted penalty function in compound Poisson risk model. use projection on Laguerre basis and we compute coefficients using Plancherel theorem. provide an upper bound MISE our estimator, show it achieves parametric rates convergence Sobolev–Laguerre spaces without needing bias-variance compromise. Moreover, compare with deconvolution metho...

This note introduces some examples of quantum random walks in R and proves the weak convergence of their rescaled n-step densities. One of the examples is called the Plancherel quantum walk because the “quantum coin flip” is the Fourier Integral (or Plancherel) Transform. The other examples are the Birkhoff quantum walks, so named because the coin flips are effected by means of measure preservi...

We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy’s space H2,A, A> 0. This gives another version of the Fourier-integral-type theorem for the Lebedev transform. The result is generalized for a weighted Hardy space Ĥ2,A ≡ Ĥ2((−A,A);|Γ(1+Rez+iτ)|2dτ), 0 < A < 1, of analytic functions f(z),z = R...

Let G be a real semisimple Lie group. Harish-Chandra has defined the Schwartz space, V[G), on G. A tempered distribution on G is a continuous linear functional on R G ) . If the real rank of G equals one, Harish-Chandra has published a version of the Plancherel formula for I^(G) [3(k), 5241. We restrict the Fourier transform map to %(G), and we compute the image of the space V(G) [Theorem 31. T...

Abstract. The focus of this paper is weighted uncertainty principle inequalities in harmonic analysis. We start by reviewing the classical uncertainty principle inequality, and then proceed to extensions and refinements by modifying two major results necessary to prove the classical case. These are integration by parts and the Plancherel theorem. The modifications are made by means of generaliz...

We consider the Robinson–Schensted–Knuth algorithm applied to a random input and study growth of bottom rows corresponding Young diagrams. prove multidimensional Poisson limit theorem for resulting Plancherel process. In this way we extend result Aldous Diaconis more than just one row. This can be interpreted as convergence multi-line Hammersley process its stationary distribution which is give...

(3) v = fdju + vc for the decomposition into discrete (ƒ dju as above) and continuous vc parts. Let F = û = J2k' + J'e' dvc{y) be the Fourier transform of the measure v. Then Wiener's theorem says (2) continues to hold. This means that the Fourier transform vc of the continuous portion of the measure does not contribute to the Bohr mean of |F|. We will interpret Wiener's theorem to mean that ev...