Sampling theory for operators motivated by the operator identification problem in communications engineering has been developed during the last few years 1–4 . In 4 , Hong and Pfander gave an operator version of Kramer’s Lemma see 4, Theorem 25 . But they did not give any explicit kernel satisfying the hypotheses in 4, Theorem 25 other than the Fourier kernel. In this paper, we present that the...

We present novel microlocal and injectivity analyses of ellipsoid hyperboloid Radon transforms. introduce a new transform, R, which defines the integrals compactly supported L2 function, f, over ellipsoids hyperboloids with centers on smooth connected surface, S. Our transform is shown to be Fourier Integral Operator (FIO) in our main theorem we prove that R satisfies Bolker condition if suppor...

The goal of this paper is to study the asymptotic behavior of almost alternating permutations, that is, permutations that are alternating except for a finite number of exceptions. Let β l1 lk denote the number of permutations which consist of l1 ascents, l2 descents, l3 ascents, and so on. By combining the Viennot triangle and the boustrophedon transform, we obtain the exponential generating fu...

Let λ be a positive number, and let (xj : j ∈ Z) ⊂ R be a fixed Riesz-basis sequence, namely, (xj) is strictly increasing, and the set of functions {R ∋ t 7→ ej : j ∈ Z} is a Riesz basis (i.e., unconditional basis) for L2[−π,π]. Given a function f ∈ L2(R) whose Fourier transform is zero almost everywhere outside the interval [−π, π], there is a unique square-summable sequence (aj : j ∈ Z), depe...

In this paper, we study the finite Gabor system for oversampling schemes. A characterization of dual tight frame using discrete time Zak transform is given. Also, a method to calculate coefficients expansion in case and necessary sufficient condition existence biorthogonal pair Riesz basis l2(ZL) Further, introduce notion block sliding Fourier (BSDFT) which reduces computational complexity give...

In an intercomprehension scenario, typically a native speaker of language L1 is confronted with output from an unknown, but related language L2. In this setting, the degree to which the receiver recognizes the unfamiliar words greatly determines communicative success. Despite exhibiting great string-level differences, cognates may be recognized very successfully if the receiver is aware of regu...

We consider the L mapping properties of a model class of strongly singular integral operators on the Heisenberg group H; these are convolution operators on H whose kernels are too singular at the origin to be of Calderón-Zygmund type. This strong singularity is compensated for by introducing a suitably large oscillation. Our results are obtained by utilizing the group Fourier transform and unif...

A complete characterization is given of closed shift-invariant subspaces of L2(Rd) which provide a specified approximation order. When such a space is principal (i.e., generated by a single function), then this characterization is in terms of the Fourier transform of the generator. As a special case, we obtain the classical Strang-Fix conditions, but without requiring the generating function to...

In this note we give a generalization of a result of Aronszajn and Smith [l] concerning sections of exceptional sets for the spaces of Bessel potentials on Rn of L2 functions and restrictions of functions in these spaces. For the sake of completeness we recall briefly the relevant definitions and theorems. We refer for details to [2]. Throughout this paper we will be concerned with functions de...