The paper covers the foundations of fractal calculus on fractal curves, defines different
function classes, establishes vector spaces for F α-integrable functions, introduces local …

In this paper, we discuss a new framework for operator-valued Gaussian processes and
their covariance kernels. Our emphasis is four-fold:(i) starting with a positive operator-valued …

Motivated by questions in quantum theory, we study Hilbert space valued Gaussian
processes, and operator-valued kernels, ie, kernels taking values in B (H)(= all bounded …

Motivated by applications, we consider here new operator theoretic approaches to
Conditional mean embeddings (CME). Our present results combine a spectral analysis …

In this paper we show how specific families of positive definite kernels serve as powerful
tools in analyses of iteration algorithms for multiple layer feedforward Neural Network …

For classes of self-affine fractal measures, we offer a new analysis of the associated
diffusions, Markov processes, semigroups, and Dirichlet forms. With view to an harmonic …

Variational inequalities form an important family of nonlinear boundary value and initial-
boundary value problems and they arise in a wide variety of applications in science and …

We study non-linear data-dimension reduction. We are motivated by the classical linear
framework of Principal Component Analysis. In nonlinear case, we introduce instead a new …

We study non-linear data-dimension reduction. We are motivated by the classical linear
framework of Principal Component Analysis. In nonlinear case, we introduce instead a new …