Discretization of continuous (analog) convolution operators by direct sampling of the convolution kernel and use of fast Fourier transforms is highly efficient. However, it assumes the input and output signals are band-limited, a condition rarely met in practice, where signals have finite support or abrupt edges and sampling is nonideal. Here, we propose to approximate signals in analog, shift-...

Computer vision operates on images that usually come in the form of arrays of pixel values. These values are invariably affected by noise, so it is useful to clean the images somewhat by an operation, called smoothing, that replaces each pixel by a linear combination of some of its neighbors. Smoothing reduces the effects of noise, but blurs the image. In the case of noise suppression, blurring...

"Making use of a modi ed Hadamard product or convolution harmonic functions with varying arguments, combined an integral operator, we study when these belong to given class. Following idea U. Bednarz and J. Sokol de ne the order consistence three classes determine it for certain arguments ned using operator."

The purpose of the present paper is to study a new subclass of harmonic univalent functions associated with fractional calculus operator. We obtain coefficient conditions, distortion bounds and extreme points for this class and discuss a class preserving integral operator. We also show that the class studied in this paper is closed under convolution and convex combination. The results obtained ...

We study Cesàro (C, δ) means for two-variable Jacobi polynomials on the parabolic biangle B = {(x1, x2) ∈ R2 : 0 ≤ x1 ≤ x2 ≤ 1}. Using the product formula derived by Koornwinder & Schwartz for this polynomial system, the Cesàro operator can be interpreted as a convolution operator. We then show that the Cesàro (C, δ) means of the orthogonal expansion on the biangle are uniformly bounded if δ > ...

Let T be the Calderón-Zygmund singular integral operator, a well-known result of Coifman et al. (see [6]) states that the commutator [b,T]( f ) = T(b f )− bT( f ) (where b ∈ BMO) is bounded on Lp(Rn) (1 < p <∞); Chanillo (see [1]) proves a similar result when T is replaced by the fractional integral operator; in [8, 9], these results on the TriebelLizorkin spaces and the case b ∈ Lipβ (where Li...

We develop a new 3D wavefield-extrapolation method for a transversely isotropic (TI) medium with a symmetry axis. The wavefield extrapolation is done by an implicit isotropic extrapolation operator with an explicit correction operator. The explicit correction is a 2D convolution operator in the space domain, whose coefficients are estimated by a weighted least-squares method in the Fourier doma...

Let T be the singular integral operator, a well-known result of Coifman, Rochberg and Weiss [6] which states that the commutator [b,T ] = T (b f )− bT f (where b ∈ BMO) is bounded on Lp(Rn)(1 < p < ∞). Chanillo [1] proves a similar result when T is replaced by the fractional integral operator. In [9,11], these results on the Triebel–Lizorkin spaces and the case b∈Lipβ (where Lipβ is the homogen...

with ∆z being a small extrapolation step. The advantage of computation in the kx, ky-ω domain is that the desired result is obtained by multiplication of the data with the operator. However, to allow laterally varying medium functions a space variant convolution operator in the x, y-ω (space-frequency) domain should be applied. When the spatial extrapolation operator is used in an explicit recu...