Poria, Anirudha Swain, Jitendriya
Published in
Advances in Pure and Applied Mathematics

Let ℍ{\mathbb{H}} be a separable Hilbert space. In this paper, we establish a generalization of Walnut’s representation and Janssen’s representation of the ℍ{\mathbb{H}}-valued Gabor frame operator on ℍ{\mathbb{H}}-valued weighted amalgam spaces Wℍ(Lp,Lvq){W_{\mathbb{H}}(L^{p},L^{q}_{v})}, 1≤p,q≤∞{1\leq p,q\leq\infty}. Also, we show that the frame...

Benayadi, Saïd Mhamdi, Fahmi
Published in
Advances in Pure and Applied Mathematics

An odd-quadratic Leibniz superalgebra is a (left or right) Leibniz superalgebra with an odd, supersymmetric, non-degenerate and invariant bilinear form. In this paper, we prove that a left (resp. right) Leibniz superalgebra that carries this structure is symmetric (meaning that it is simultaneously a left and a right Leibniz superalgebra). Moreover...

Ghoul, Tej-Eddine Nguyen, Van Tien Zaag, Hatem
Published in
Advances in Pure and Applied Mathematics

In this note, we consider the semilinear heat system ∂tu=Δu+f(v),∂tv=μΔv+g(u),μ>0,\partial_{t}u=\Delta u+f(v),\quad\partial_{t}v=\mu\Delta v+g(u),\quad\mu>0, where the nonlinearity has no gradient structure taking of the particular form f(v)=v|v|p-1 and g(u)=u|u|q-1 with p,q>1,f(v)=v\lvert v\rvert^{p-1}\quad\text{and}\quad g(u)=u\lvert ...

Baklouti, Ali
Published in
Advances in Pure and Applied Mathematics

Ogbuisi, Ferdinard U. Mewomo, Oluwatosin T.
Published in
Advances in Pure and Applied Mathematics

In this paper, we introduce an iterative scheme involving an inertial term and a step size independent of the operator norm for approximating a solution to a split variational inequality problem in a real Hilbert space. Furthermore, we prove a convergence theorem for the sequence generated by the proposed operator norm independent inertial accelera...

Monzón, Gabriel
Published in
Advances in Pure and Applied Mathematics

We propose a finite element approximation for a fourth-order Steklov eigenvalue problem by means of the virtual elements. In this setting we derive error estimates for the eigenvalues and eigenfunctions under standard assumptions on the domain.

Alomari, Mohammad W.
Published in
Advances in Pure and Applied Mathematics

In this work, an operator version of Popoviciu’s inequality for positive operators on Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique, an operator version of Popoviciu’s inequality for convex functions is obtained. Some other related inequalities are also presented.

Kieburg, Mario Forrester, Peter J. Ipsen, Jesper R.
Published in
Advances in Pure and Applied Mathematics

The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a polynomial ensemble. It is furthermore the case that the corresponding bi-orthogonal system can be determined in ter...

Shams Yousefi, Marzieh
Published in
Advances in Pure and Applied Mathematics

A non-trivial multi-norm structure based on the enveloping C*{C^{*}}-algebras will be discussed in this paper. The main example is group C*{C^{*}}-algebras on compact groups. Also a (generalizing) non-trivial multi-norm structure based on the Fourier and Fourier–Stieltjes algebras on compact groups will be given.

Djafri, S. Moussaoui, Toufik
Published in
Advances in Pure and Applied Mathematics

In this paper, we are interested in the study of the existence of positive solutions for the following nonlinear boundary value problem on the half-line: {-u′′(x)=q(x)f(x,u,u′),x∈(0,+∞),u′(0)=u′(+∞)=0,\left\{\begin{aligned} \displaystyle-u^{\prime\prime}(x)&\displaystyle=q(x)f(x% ,u,u^{\prime}),&&\displaystyle x\in(0,+\infty),\\ \displaystyle...