In [M. K. Vemuri, Realizations of the canonical representation, submitted], it was shown that the spectral synthesis problem for the Alpha transform is closely related to the problem of classifying realizations of the canonical representation (of the Heisenberg group). In this paper, we show that discrete sets are sets of spectral synthesis for the Alpha transform.

We primarily consider here the L mapping properties of a class of strongly singular Radon transforms on the Heisenberg group H; these are convolution operators on H with kernels of the form M(z, t) = K(z)δ0(t) where K is a strongly singular kernel on C . Our results are obtained by utilizing the group Fourier transform and uniform asymptotic forms for Laguerre functions due to Erdélyi. We also ...

Under certain conditions on an integrable function P having a real-valued Fourier transform P̂ and such that P(0)=0, we obtain an estimate which describes the oscillation of P̂ in [−C‖P ′‖∞/‖P ‖∞, C‖P ′‖∞/‖P ‖∞], whereC is an absolute constant, independent of P. Given > 0 and an integrable function with a non-negative Fourier transform, this estimate allows us to construct a finite linear combina...

With the rapid developments of higher resolution imaging systems, larger image data are produced. To process the increasing image data with conventional methods, the processing time increases tremendously. Image segmentation is one of the many image processing algorithms, and it is widely used in medical imaging (i.e. find tumor in MRI), robotic vision (i.e. vision-based navigation), and face r...

An efficient algorithm for computing the one-dimensional partial fast Fourier transform fj = ∑c(j) k=0 e Fk is presented. Naive computation of the partial fast Fourier transform requires O(N) arithmetic operations for input data of length N . Unlike the standard fast Fourier transform, the partial fast Fourier transform imposes on the frequency variable k a cutoff function c(j) that depends on ...

This paper presents a study of automatic detection and recognition of bird species based on bioacoustics. The energy distribution in different frequency bands varies quite significantly among different birds’ sounds. Energy in various frequency bands is extracted using wavelet packet transform and k-nearest neighbor algorithm is used for classification. In our experiment, classification accurac...

We show that the transformation of D-branes under T-duality on fourtorus is represented by Nahm transform of instantons. The argument for this allows us to generalize Nahm transform to the case of orthogonal and symplectic gauge groups as well as to instantons on Z2 orbifold of four-torus. In addition, we identify the isomorphism of K-theory groups that realizes the transformation of D-brane ch...

The reaction cross section of a bimolecular reaction has been calculated from the corresponding rate constant by the inverse Laplace transform. In carrying out the inverse Laplace transform, the method of steepest-descent has been used. As applications, the reaction cross sections for the rate constant of k(T) = k' T(n)e(-E0/kT) and for the rate constant of the absolute reaction rate theory hav...

In this paper, the k-trigonometric functions over the Galois Field GF(q) are introduced and their main properties derived. This leads to the definition of the cask(.) function over GF(q), which in turn leads to a finite field Hartley Transform . The main properties of this new discrete transform are presented and areas for possible applications are mentioned.

As the capacity to summarize of the preference map diminishes with the number of consumers (the number of axes to interpret increases), a non-metric PCA is sometimes used to reduce the number of necessary axes. The non-metric PCA consists of a monotone transform of the data so that the variability explained by the k (k=2 or 3) first axes is maximized. This transform implies that we consider the...