In this paper, concept of fuzzy continuous operator, bounded linear operator are introduced in strong [Formula: see text]-b-normed spaces and their relations studied. Idea norm is developed completeness BF(X,Y) established.

It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(−A)1/2 generates a bounded C0-group. The proof uses a transference principle for cosine functions.

We study one-dimensional lattices of weakly coupled piecewise expanding interval maps as dynamical systems. Since neither the local maps need to have full branches nor the coupling map needs to be a homeomorphism of the infinite dimensional state space, we cannot use symbolic dynamics or other techniques from statistical mechanics. Instead we prove that the transfer operator of the infinite dim...

We consider a scalar conservation law in the quarter plane. This equation is approximated in a continuous kinetic Bhatnagar-Gross-Krook (BGK) model. The convergence of the model towards the unique entropy solution is established in the space of functions of bounded variation, using kinetic entropy inequalities, without special restriction on the flux nor on the equilibrium problem’s data. As an...

We obtain sufficient conditions for a densely-defined operator on the Fock space to be bounded or compact. Under the boundedness condition we then characterize the compactness of the operator in terms of its Berezin transform.

We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type.

If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...

We describe the transfer operator approach to coupled map lattices (CML) in cases where the local map is expanding but has no Markov partition (e.g. a general tent map). The coupling is allowed to be non-local, but the total innuence of all sites j 6 = i on site i must be small. The main technical tool are lattice-size independent estimates of Lasota-Yorke type which show that the transfer (Per...

In the present paper, we study some approximation properties of the Szász type operators involving Charlier polynomials introduced by Varma and Taşdelen in 2012. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain the error in the approximation of functions having derivatives of bounded variation.

We study one-dimensional lattices of weakly coupled piecewise expanding interval maps as dynamical systems. Since neither the local maps need to have full branches nor the coupling map needs to be a homeomorphism of the infinite dimensional state space, we cannot use symbolic dynamics or other techniques from statistical mechanics. Instead we prove that the transfer operator of the infinite dim...