This paper provides a theoretical analysis of a higher-order, FFT-based integral equation method introduced recently [IEEE Trans. Antennas and Propagation, 48 (2000), pp. 1862–1864] for the evaluation of transverse electric–polarized electromagnetic scattering from a bounded, penetrable inhomogeneity in two-dimensional space. Roughly speaking, this method is based on Fourier smoothing of the in...

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*}  mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*}  ma...

Traditional methods of time-frequency and multiscale analysis, such as wavelets and Gabor frames, have been successfully employed for representing most classes of pseudodifferential operators. However these methods are not equally effective in dealing with Fourier Integral Operators in general. In this paper, we show that the shearlets, recently introduced by the authors and their collaborators...

We study the boundedness of bilinear Fourier integral operators on products of Lebesgue spaces. These operators are obtained from the class of bilinear pseudodifferential operators of Coifman and Meyer via the introduction of an oscillatory factor containing a real-valued phase of five variables Φ(x, y1, y2, ξ1, ξ2) which is jointly homogeneous in the phase variables (ξ1, ξ2). For symbols of or...

In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse proble...

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

the aim of this paper is to prove new quantitative uncertainty principle for the generalized fourier transform connected with a dunkl type operator on the real line. more precisely we prove an lp-lq-version of morgan&apos;s theorem.

Classical integral operators usually display invariance with respect to orthogonal transformations. If the domain of an operator equation is symmetric with respect to some orthogonal transformations, then appropriate discretiza-tions of the operator equation lead to system matrices which are equivariant with respect to a group of permutations. This property can be exploited to design eecient me...