We construct a pointwise Boutet de Monvel-Sj\"ostrand parametrix for the Szeg\H{o} kernel of weakly pseudoconvex three dimensional CR manifold finite type assuming range its tangential operator to be closed; thereby extending earlier analysis Christ. This particularly extends Fefferman's boundary asymptotics Bergman domains in $\mathbb{C}^{2}$, agreement with D'Angelo's example. Finally our res...

Making use of complex analytic techniques as well methods involving weight functions, we study a few equivalent conditions Hilbert-type integral inequality with nonhomogeneous kernel and parameters. In the form applications deduce homogeneous kernel, additionally consider operator expressions.

This paper presents a detailed study and comparison of some Kernelized Fuzzy C-means Clustering based image segmentation algorithms Four algorithms have been used Fuzzy Clustering, Fuzzy CMeans(FCM) algorithm, Kernel Fuzzy CMeans(KFCM), Intuitionistic Kernelized Fuzzy CMeans(KIFCM), Kernelized Type-II Fuzzy CMeans(KT2FCM).The four algorithms are studied and analyzed both quantitatively and qual...

Abstract By the use of weight coefficients and techniques real analysis, we establish a new Hardy–Mulholland-type inequality with mixed kernel best possible constant factor in terms hypergeometric function. Equivalent forms, an operator expression norm reverses are also considered.

Let μ be a nonnegative Radon measure on R which only satisfies the following growth condition that there exists a positive constant C such that μ B x, r ≤ Cr for all x ∈ R, r > 0 and some fixed n ∈ 0, d . In this paper, the authors prove that for suitable indexes ρ and λ, the parametrized g∗ λ function M∗,ρ λ is bounded on L μ for p ∈ 2,∞ with the assumption that the kernel of the operator M∗,ρ...

We describe how to use Schoenberg’s theorem for a radial kernel combined with existing bounds on the approximation error functions for Gaussian kernels to obtain a bound on the approximation error function for the radial kernel. The result is applied to the exponential kernel and Student’s kernel. To establish these results we develop a general theory regarding mixtures of kernels. We analyze t...