On a general q-Fourier transformation with nonsymmetric kernels

Some Integral Equations with Nonsymmetric Separable Kernels*

Absbact. It is shown that the eigeovalues and eigenfunctions for the class of "separable" or "semidegenerate" kernels can be determined from the solution of a linear differential equation, which is usually more amenable to machine solution. The theory is extended to solve a simultaneous diagonalization problem for two separable kernels. Finally, some new connections are obtained between Riccati...

Learning with Transformation Invariant Kernels

This paper considers kernels invariant to translation, rotation and dilation. We show that no non-trivial positive definite (p.d.) kernels exist which are radial and dilation invariant, only conditionally positive definite (c.p.d.) ones. Accordingly, we discuss the c.p.d. case and provide some novel analysis, including an elementary derivation of a c.p.d. representer theorem. On the practical s...

Ranking with Kernels in Fourier space

In typical ranking problems the total number n of items to be ranked is relatively large, but each data instance involves only k << n items. This paper examines the structure of such partial rankings in Fourier space. Specifically, we develop a kernel–based framework for solving ranking problems, define some canonical kernels on permutations, and show that by transforming to Fourier space, the ...

On a General $q$-identity

In this paper, by means of the q-Rice formula we obtain a general q-identity which is a unified generalization of three kinds of identities. Some known results are special cases of ours. Meanwhile, some identities on q-generalized harmonic numbers are also derived.

On General Lips hitzian Kernels