We construct bivariate biorthogonal cosine wavelets on a twooverlapping rectangular grid with bell functions not necessary of tensor product type. The biorthogonal system as well as frame and Riesz basis conditions are given explicitly. Our methods are based on the properties of bivariate total folding and unfolding operators.

In this paper we have used double infinite matrix A = (ailjk) of real numbers to define the A-frame. Some results on Riesz basis and A-frame also have been studied. This Work is motivated from the work of Moricz and Rhoades [7]. 2001 AMS Classification. Primary 41A17, Secondary 42C15.

In this paper we construct infinitely many selfadjoint solutions of the control algebraic Riccati equation using invariant subspaces of the associated Hamiltonian. We do this under the assumption that the system operator is normal and has compact inverse, and that the Hamiltonian possesses a Riesz basis of invariant subspaces.

We study the stability of weakly coupled and partially damped systems by means of Riesz basis approach in higher dimension spaces. We propose a weaker distributed damping that compensates the behaviour of the eigenvalues of the system, therefore gives the optimal polynomial energy decay rate for smooth initial data.

A framework of a general type of Petrovsky equation is formulated. The characteristic equation for eigenvalues of the system is derived and the associated eigenfunctions are found. For N connected beams with linear feedbacks at joint points, the asymptotic expansions of eigenvalues and eigenfunctions are further developed, and the Riesz basis property and the exponential stability are then conc...

Continuing in the vein of a recently developed generalization of continuum thermomechanics, in this paper we extend fracture mechanics and beam mechanics to materials described by fractional integrals involving D, d and R. By introducing a product measure instead of a Riesz measure, so as to ensure that the mechanical approach to continuum mechanics is consistent with the energetic approach, sp...

recently, mohiuddine and alghamdi introduced the notion of lacunary statistical convergence in a locally solid riesz space and established some results related to this concept. in this paper, some inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences are established and extensions of a decomposition theorem, a tauberian theorem to the l...

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-valued (primary) wavelet basis of L(2) (R(2)) into a complex one. The Riesz operator is also steerable in the sense that it give access to the Hil...

It is known [6], [14], [19] that if Ω⊂Rd belongs to a class of k-tiling domains when translated by lattice Λ, there exists Riesz basis exponentials for L2(Ω) constructed using k translates the dual Λ⁎. In this paper, we give an explicit construction corresponding biorthogonal basis. We also extend iterative reconstruction algorithm introduced in [11] setting.