In this work, by combining Carlson-type and Nash-type inequalities for the Weinstein transform $\mathscr{F}_W$ on $\mathbb{K}=\mathbb{R}^{d-1}\times[0,\infty)$, we show Laeng-Morpurgo-type uncertainty inequalities. We establish also local-type $\mathscr{F}_W$, deduce a Heisenberg-Pauli-Weyl-type inequality transform.

A perturbation algorithm using any time transformation is introduced. To account for the nonlinear dependence of the function, we exhibit the function f of the system in the differential equation. To this end, we introduce the transformation t t w f Te ) , ( , where f is a function that depends on t or w. The problems are solved with new time transformation: Linear damped vibration equation, cl...

1. A direct fluorescent antibody (F.A.) tech­nique for diagnosis of Gonococci is de­scribed. 2. The results of applying F.A. method in the 270 female cases are presented and compared with the conventional method find­ings. 3. 220 cases were diagnosed by one or more methods at the first examinations. F .A. tests alone were positive in 44 ,eases and .F .A. direct diagnosis was made in a tot...

We establish the various relationships that exist among the integral transform Ᏺ α,β F , the convolution product (F * G) α , and the first variation δF for a class of functionals defined on K[0,T ], the space of complex-valued continuous functions on [0,T ] which vanish at zero. 1. Introduction and definitions. In a unifying paper [10], Lee defined an integral transform Ᏺ α,β of analytic functi...

An uncertainty principle, due to Hardy, for Fourier transform pairs on R says that if the function f is “very rapidly decreasing”, then the Fourier transform cannot also be “very rapidly decreasing” unless f is identically zero. In this paper we state and prove an analogue of Hardy’s theorem for the ndimensional Euclidean motion group.

The mathematics behind Computerized Tomography (CT) is based on the study of the parallel beam transform P and the divergent beam transform D. Both of these map a function f in Rn into a function defined on the set of all lines in Rn, by integrating f along these lines. The parallel and divergent k-plane transforms are defined in a similar fashion by integration over k-planes (i.e., translates ...

In this paper, we focus on application of fuzzy transform (F-transform) to analysis of time series under the assumption that the latter can be additively decomposed into trend-cycle, seasonal component and noise. We prove that when setting properly width of the basic functions, the inverse F-transform of the time series closely approximates its trend-cycle. This means that the F-transform almos...

Fourier transform is among the most widely used tools in computer science. Computing the Fourier transform of a signal of length N may be done in time Θ(N logN) using the Fast Fourier Transform (FFT) algorithm. This time bound clearly cannot be improved below Θ(N), because the output itself is of length N . Nonetheless, it turns out that in many applications it suffices to find only the signifi...

{ This paper presents a model of nite Radon transforms composed of Radon projections. The model generalizes to nite groups projections in the classical Radon transform theory. The Radon projector averages a function on a group over cosets of a subgroup. Reconstruction formulae formally similar to the convolved backprojection ones are derived and an iterative reconstruction technique is found to...

This paper proposes a new correlation analysis method for nonstationary and energy-limited continual signals, which works out a formula similar to time correlation theory; that is to say when the operator, , meets a certain condition, its auto-correlation property of Fourier transform can be presented by Fourier transform of its energy function, f 2 ) ( t f , revealing its correlation of the Fo...