We present inequalities related to generalized matrix function for positive semidefinite block matrices. introduce partial functions corresponding traces, and then provide a unified extension of the recent due Lin [Electron. J. Linear Algebra 27 (2014) 821-826], Zhang et al. [Linear Appl. 498 (2016) 99-105] 332-341] result Choi 532 (2017) 1-7]. Moreover, we demonstrate application $3\times 3$ m...

In-memory computing using emerging technologies such as Resistive Random-Access Memory (ReRAM) has been proposed a promising substitute for future applications to address the ‘von Neumann bottleneck’. Multiplication is key component inner product computation in every digital signal processing (DSP) application and complexity of multipliers increases greatly with bit-width. Distributed arithmeti...

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)~∑...

This paper proposes an inductive method to construct bases for spaces of spherical harmonics over the unit sphere Ω2q of Cq. The bases are shown to have many interesting properties, among them orthogonality with respect to the inner product of L(Ω2q). As a bypass, we study the inner product [f, g] = f(D)(g(z))(0) over the space P(Cq) of polynomials in the variables z, z ∈ Cq, in which f(D) is t...

We show that to each linear solution that has the inessential game property, there is an inner product on the space of games such that the solution to each game is the best additive approximation of the game (w.r.t. the norm derived from this inner product). If the space of games has an inner product, then the function that to each game assigns the best additive approximation of this game (w.r....