Work

Conditional Exponential Convex Functions on White Noise Spaces

Year: 2025

Type: article

Abstract: This paper seeks to present the fundamental features of the category of conditional exponential convex functions (CECFs). Additionally, the study of continuous CECFs contributes to the characterization of convolution semigroups. In this context, we expand our focus to include a much broader class of Gaussian processes, where we define the generalized Fourier transform in a more straightforward manner. This approach is closely connected to the method by which we derived the Gaussian process, utilizing the framework of a Gelfand triple and the theorem of Bochner–Minlos. A part of this work involves constructing the reproducing kernel Hilbert spaces (RKHS) directly from CECFs.

Source: Axioms

DOI: 10.3390/axioms14030223

Authors: Ahmed. M. Zabel, Areej A. Almoneef, Ayat Nassar, Abd-Allah Hyder

Institutions: Al-Azhar University, Princess Nourah bint Abdulrahman University, Kafrelsheikh University, King Khalid University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: Princess Nourah Bint Abdulrahman University, King Khalid University