In this paper we consider the system of functions G_(r,n)^α (x) (r∈N,n=0,1,…) which is orthogonal with respect to Sobolev-type inner product on (-1,1) and generated by Gegenbauer polynomials. The main goal work study some properties related {φ_(k,r) (x)}_(k≥0) {G_(r,n)^α (x)} functions. We conditions a function f(x) given in generalized for it be expandable into mixed Fourier series form f(x)~∑...

We propose a framework for dealing with binary hard-margin classification in Banach spaces, centering on the use of a supporting semi-inner-product (s.i.p.) taking the place of an inner-product in Hilbert spaces. The theory of semi-inner-product spaces allows for a geometric, Hilbert-like formulation of the problems, and we show that a surprising number of results from the Euclidean case can be...

A simple derivation of a meaningful, manifestly covariant inner product for real KleinGordon (KG) fields with positive semi-definite norm is provided which turns out — assuming a symmetric bilinear form — to be the real-KG-field limit of the inner product for complex KG fields reviewed by A. Mostafazadeh and F. Zamani in December, 2003, and February, 2006 (quant-ph/0312078, quant-ph/0602151, qu...

Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of datadriven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption, and might be identifiable under severe obfuscation. Our approach is based on uncovering a valid complete inner product on the space of ergodic stationary finite...

In this paper, we introduce the concept of family of local atoms in a 2-inner product space and then this concept is generalized to an atomic system. Besides, a characterization of an atomic system lead to obtain a new frame. Actually this frame is a generalization of previous works.

This work aims to develop a new class of accretive mappings and investigate its associated proximal mappings. is known as generalized (Hk,φ)-η-accretive Further, the research includes discussion application, leading set-valued variational-like inclusions (SVVLI, in short) semi-inner product spaces. The corresponding fixed point problem for SVVLI given. used provide an iterative scheme solving S...