Preserving Properties of the Double Integral Operators

In the present paper, we obtain some subordination- and superordination-preserving properties of certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorems for these integral operators are also considered.

In the present paper, a characterization of the Favard classes for the sampling Kantorovich operators based upon bandlimited kernels has been established. In order to achieve the above result, a wide preliminary study has been necessary. First, suitable high order asymptotic type theorems in L^p-setting, 1 le p le +infty , have been proved. Then, the regularization properties of the sampling Kantorovich operators have been investigated. Here, we show how the regularity of the kernel influences the operator itself; this has been shown for bandlimited kernels, or more in general for kernels in Sobolev spaces, satisfying a Strang-Fix type condition of order r in mathbb {N}^+. Further, for the order of approximation of the sampling Kantorovich operators, quantitative estimates based on the L^p modulus of smoothness of order r have been established. As a consequence, the qualitative order of approximation is also derived assuming f in suitable Lipschitz and generalized Lipschitz classes. Moreover, an inverse theorem of approximation has been stated, allowing to obtain a full characterization of the Lipschitz and of the generalized Lipschitz classes in terms of convergence of the above sampling type series. These approximation results have been proved for not necessarily bandlimited kernels. From the above mentioned characterization, it remains uncovered the saturation case that, however, can be treated by a totally different approach assuming that the kernel is bandlimited. Indeed, since sampling Kantorovich (discrete) operators based upon bandlimited kernels can be viewed as double-singular integrals, exploiting the properties of the convolution in Fourier Analysis, we become able to get the desired result obtaining a complete overview of the approximation properties in L^p(mathbb {R}), 1 le p le +infty , for the sampling Kantorovich operators.

Let w and \omega be two weight functions on R^{2d} and 1 \leq p,q \leq \infty. Also let M(p,q,\omega) (R^d) denote the subspace of tempered distributions S' (R^d) consisting of f \in S' (R^d) such that the Gabor transform V_g f of f is in the weighted Lorentz space L(p,q,\omega d\mu) (R^{2d}) . In the present paper we define a space Q_{g,w}^{M(p,q,\omega) (R^d) as counter image of M(p,q,\omega) (R^d) under Toeplitz operator with symbol w. We show that Q_{g,w}^{M(p,q,\omega)}(R^d) is a generalization of usual Sobolev-Shubin space Q_s (R^d). We also investigate the boundedness and Schatten-class properties of Toeplitz operators.

In recent years Russian specialists have developed industrial weldable aluminum alloys alloyed with a small amount of scandium. Scandium added to existing weldable aluminum alloys improves considerably the set of their operational properties. In addition, the presence of scandium makes it possible to create new materials superior to traditional aluminum alloys. The present paper is devoted to problems of simultaneous alloying of aluminum alloys with scandium and zirconium.

In the present paper we state some approximation theorems concerning pointwise convergence and its rate for a class of non-convolution type nonlinear integral operators of the form: $$ T_\lambda \left( {f;x} \right) = \int\limits_A^B {K_\lambda \left( {t,x,f\left( t \right)} \right)dt , x \in } \left\langle {a,b} \right\rangle ,\lambda \in \Lambda $$. In particular, we obtain the pointwise convergence and its rate at some characteristic points x 0 of f as (x, λ) ar(x 0, λ0) in L 1 〈 A,B 〉, where 〈 a,b 〉 and 〈 A,B 〉 are is an arbitrary intervals in R, Λ is a non-empty set of indices with a topology and λ0 an accumulation point of Λ in this topology.The results of the present paper generalize several ones obtained previously in the papers [19]–[23].

In this paper we investigate several interesting properties of the fractional calculus operators, the Carlson-Shaffer linear operator L(a,c) and a certain integral operator , associated with various subclasses of analytic and univalent functions. We also investigate the relationships of some of these classes with the Hardy space H ∞ (of bounded analytic functions in the open unit disk μ and with some families of multiplier transformations.

In the present paper we consider the little-known Sampson operator that is strongly elliptic and self-adjoint second order differential operator acting on covariant symmetric tensors on Riemannian manifolds. First of all, we review the results on this operator. Then we consider the properties of the Sampson operator acting on one-forms and symmetric two-tensors. We study this operator using the analytical method, due to Bochner, of proving vanishing theorems for the null space of a Laplace operator admitting a Weitzenb?ck decomposition. Further we estimate operator?s lowest eigenvalue.

In the present paper we propose q-analogue of the well known Szasz-Kantorovich operators. We study local approximation as well as weighted approximation properties of these new operators.

The present paper is devoted to the study of exponential stabilization of a one-dimensional thermoelastic diffusion problem of type II for isotropic and homogeneous materials with frictional damping and time delay. The system of equations under consideration is a coupling of three hyperbolic equations involving three variables considering frictional damping and time delay on each variable. Using semigroup theory, we prove the well-posedness by the Lumer–Phillips theorem and the exponential stability by exploring the dissipative properties of the linear operator associated with the model through the Gearhart–Huang–Pruss theorem.

In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, we first give approximation properties of such operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we present approximation properties of weighted spaces. Finally, we obtain the Voronovskaya type theorem of this operator.

In the present paper we consider bounded linear operators which have orbits dense relative to nontrivial subspaces. We give nontrivial examples of such operators and establish many of their basic properties. An example of an operator which has an orbit dense relative to a certain subspace but is not subspace-hypercyclic for this subspace is given. This, in turn, provides a new answer to a question posed in [18]. Other hypercyclic-like properties of such operators are also considered.

It was known that orthogonality preserving property and surjectivity of nonlinear Markov operators, acting on finite dimensional simpleces, are equivalent. It turns out that these notions are no longer equivalent when such kind of operators are considered over on infinite dimensional spaces. In the present paper, we find necessary and sufficient condition to be equivalent of these notions, for the second order nonlinear Markov operators. To do this, we fully describe all surjective second order nonlinear Markov operators acting on infinite dimensional simplex. As an application of this result, we provided some sufficient conditions for the existence of positive solutions of nonlinear integral equations whose domain are not compact.

A General family of integral operators and associated subordination and superordination properties of some special analytic function classes

A mixed boundary value problem for the stationary heat transfer partial differential equation with variable coefficient in an exterior domain is reduced to some systems of direct segregated parametrix-based boundary-domain integral equations. We use a parametrix different from the one employed in some previous papers. Mapping properties of the potential type integral operators appearing in these equations are presented in appropriate Sobolev spaces. We prove the equivalence between the original BVP and the corresponding BDIE systems. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed.

We consider non-standard generalized Holder spaces of functions defined on a segment of the real axis, whose local continuity modulus has a majorant varying from point to point. We establish some properties of fractional integration operators of variable order acting from variable generalized Holder spaces to those with a “better” majorant, as well as properties of fractional differentiation operators of variable order acting from the same spaces to those with a “worse” majorant.