l1-SPIRiT is a fast magnetic resonance imaging (MRI) method which combines parallel imaging (PI) with compressed sensing (CS) by performing a joint l1-norm and l2-norm optimization procedure. The original l1-SPIRiT method uses two-dimensional (2D) Wavelet transform to exploit the intra-coil data redundancies and a joint sparsity model to exploit the inter-coil data redundancies. In this work, w...

_ Processors speed is much faster than memory; to bridge this gap cache memory is used. This paper proposes a preeminent pair of replacement algorithms for Level 1 cache (L1) and Level 2 cache (L2) respectively for the Fast Fourier Transform (FFT). The access patterns of L1 and L2 are different, when CPU does not get the desired data in L1 then it refers to L2. Thus the replacement algorithm wh...

some estimates are proved for the generalized fourier-bessel transform in the space (l^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

An approximation of the Fourier Sine Transform via Grüss, Chebychev and Lupaş integral inequalities and application for an electrical curcuit containing an inductance L, a condenser of capacity C and a source of electromotive force E0P (t), where P (t) is an L2−integrable function, are given.

A generalized filter construction is used to build non-MRA Parseval wavelets for dilation by 2 in L2(R2). These examples have the same multiplicity functions as wavelet sets, yet can be made to be Cr with Cr Fourier transform for any fixed positive integer r.

A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform on the real line is proved. To this end we state, in terms of Bessel functions, an orthonormal system which is complete in L2((−1, 1), |x|2α+1 dx). This orthonormal system is a generalization of the classical exponential system defining Fourier series.

Assume ψ ∈ L(R) has Fourier transform continuous at the origin, with ψ̂(0) = 1, and that ∑ l∈Z |ψ̂(ξ − l)| 2 is bounded as a function of ξ ∈ R. Then every function f ∈ L(R) can be represented by an affine series f = ∑ j>0 ∑ k∈Z cj,kψj,k for some coefficients satisfying ‖c‖l1(l2) = ∑

We use Mellin transforms to compute a full asymptotic expansion for the tail of the Laplace transform of the squared L2-norm of any multiply-integrated Brownian sheet. Through reversion we obtain corresponding strong small-deviation estimates. AMS 2000 subject classifications. Primary 60G15, 41A60; secondary 60E10, 44A15, 41A27.

Feynman-Kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of Markov processes. General gauge and conditional gauge theorems are established for such transforms. Furthermore, the L2-infinitesimal generator of the Schrödinger semigroup given by a non-local Feynman-Kac transform is determined in terms of its associated bilinear form.

We find the minimal real number k such that the kth power of the Fourier transform of any continuous, orbital measure on a classical, compact Lie group belongs to l2. This results from an investigation of the pointwise behaviour of characters on these groups. An application is given to the study of Lp-improving measures.