The Hartley transform generalizes to the fractional (FRHT) which gives various uses in different fields of image encryption. Unfortunately, available literature is unable provide its inversion theorem. So accordingly original function cannot retrieve directly, restrict applications. intension this paper propose theorem overcome drawback. Moreover, some properties are discussed paper.

We propose a matrix approach to the computation of BattleLemarié's wavelets. The Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a B-spline of order m . The polynomial is the symbol of a bi-infinite matrix B associated with a B-spline of order 2m . We approximate this bi-infinite ma...

For a polynomial P (ξ) in ξ in R with constant complex coefficients, the operator defined by R(z)f = F((P (·)−z)f̂), where ∧ denotes the Fourier transform and F denotes its inverse, is not bounded from L to L when z is in the spectrum of P (D). What are suitable spaces B and C so that R(z) is bounded from B to C? When P (ξ) is simply characteristic, we prove that the operator R(z) is bounded fro...

We present a new inversion formula for the classical, finite, and asymptotic Laplace transform f̂ of continuous or generalized functions f . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of f̂ evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sens...

Introducing a suitable variational formulation for the local error of scattered data interpolation by radial basis functions (r), the error can be bounded by a term depending on the Fourier transform of the interpolated function f and a certain \Kriging function", which allows a formulation as an integral involving the Fourier transform of. The explicit construction of locally well{behaving adm...

We propose a new automatic program inversion method for imperative programs that contain loops. In particular, given a loop that produces an output state given a particular input state, our method can synthesize an inverse loop that reconstructs the input state given the original loop’s output state. The synthesis process consists of two major components: (a) building the inverse loop’s body, a...

The Sommerfeld integral inversion method for the Helmholtz equation in an angular region with diierent boundary values leads to boundary value problems in an innnite strip of the complex plane. We investigate a generic system for such boundary value problems and give existence and uniqueness results with optimal growth estimates on the solution. We also give the solutions of the Dirichlet probl...