Let G be a nite group and f any complex-valued function deened on G and an irreducible complex matrix representation of G. The Fourier transform of f at is deened to be the matrix P s2G f(s)(s). The Fourier transforms of f at all the irreducible representations of G determine f via the Fourier inversion formula f(s) = 1 j Gj P d trace(b f()(s ?1)): Direct computation of all Fourier transforms o...

We discuss properties of a generalized Minkowski-Funk transform de…ned for a family of hypersurfaces. We prove two-side estimates for the integral operator and show that the range conditions can be written in terms of the reciprocal Funk transform. Some applications to the spherical mean transform are considered. 1 Families of hypersurfaces Let X and be smooth manifolds of dimension n > 1 and F...

Let f be a function from Zq to Zq. Such a function f is bent if all values of its Fourier transform have absolute value 1. Bent functions are known to exist for all pairs (m, q) except when m is odd and q ≡ 2 (mod 4) and there is overwhelming evidence that no bent function exists in the latter case. In this paper the following problem is studied: how closely can the largest absolute value of th...

The Radon transform on a group A is a linear operator on the space of functions /: A-+ C. It is shown that if A = Z;: then the Radon transform with respect to a subset B c .4 is not invertible if and only if B has the same number of elements in every coset of some maximal subgroup of A. The same does not hold in general for arbitrary finite abelian groups. ' IW7 ACxhlK I%\\. 1°C Let A be a fini...

By using a particular class of directional wavelets namely, the conical wavelets, which are wavelets strictly supported in a proper convex cone in the k-space of frequencies , in this paper, it is shown that a tempered distribution is obtained as a finite sum of boundary values of analytic functions arising from the complexification of the translational parameter of thewavelet transform. Moreov...

In the present paper a Korovkin-type theorem is proposed for the approximation operators defined by the inverse Ftransforms. These results allow us to choose between a variety of shapes to be used as atoms of the fuzzy partitions used within the F-transform’s framework. In this way we can enlarge considerably the class of F-transforms proposed recently by I. Perfilieva. The new fuzzy partitions...

In this paper, we consider a special V-line transform. It integrates given function f over the V-lines whose centers are on circle centered at origin and symmetric axes pass through origin. We derive two sampling scheme of transform: standard interlaced ones. prove an error estimate for schemes, which is explicitly expressed in term f.

Using elementary arguments based on the Fourier transform we prove that for 1 ≤ q < p < ∞ and s ≥ 0 with s > n(1/2 − 1/p), if f ∈ L(R) ∩ Ḣ(R) then f ∈ L(R) and there exists a constant cp,q,s such that ‖f‖Lp ≤ cp,q,s‖f‖ θ Lq,∞‖f‖ 1−θ Ḣs , where 1/p = θ/q+(1− θ)(1/2− s/n). In particular, in R we obtain the generalised Ladyzhenskaya inequality ‖f‖L4 ≤ c‖f‖ 1/2 L2,∞ ‖f‖ 1/2 Ḣ1 . We also show that f...

where a(u, v) denotes the standard deviation of a coefficient. The inverse transform is given by The maximum coefficient value for the cosine transform can be derived from (1) as (3) (2) for w = <P for w = 1, 2, "', N-1. [ (2j + 1)U1T] [(2k + 1)V1T] • cos cos 2N 2N 1 !v' 2 I X I! p(x; u , v) = exp-Vi a(u, v) a(u, v) 1 C(w) = Vi N-1N-1 fO, k) = ~ ~ C(u)C(v)F(u, v) u=O v=O for i, k = 0, 1, "', N-...