The Property (DN) and the Exponential Representation of Holomorphic Functions.
A remark on Nilsson type integrals
We investigate ramification properties with respect to parameters of integrals (distributions) of a class of singular functions over an unbounded cycle which may intersect the singularities of the integrand. We generalize the classical result of Nilsson dealing with the case where the cycle is bounded and contained in the set of holomorphy of the integrand. Such problems arise naturally in the study of exponential representation at infinity of solutions to certain PDE's (see [Z]).
Existence result for a semilinear parametric problem with Grushin type operator.
On an extension of Shapiro's cyclic inequality.
Existence of solutions for a nonlinear degenerate elliptic system.
The integral wavelet transform in weighted Sobolev spaces.
The convergence estimates for Galerkin-wavelet solution of periodic pseudodifferential initial value problems.
On solutions of integral equations with analytic kernels and rotations
We deal with a class of integral equations on the unit circle in the complex plane with a regular part and with rotations of the form (*) x(t) + a(t)(Tx)(t) = b(t), where and are of the form (3) below. We prove that under some assumptions on analytic continuation of the given functions, (*) is a singular integral equation for m odd and is a Fredholm equation for m even. Further, we prove that T is an algebraic operator with characteristic polynomial . By means of the Riemann boundary value...
Global attractor of the Cauchy problem for a semilinear degenerate damped hyperbolic equation involving the Grushin operator
The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate damped hyperbolic equation involving the Grushin operator with a locally Lipschitz nonlinearity satisfying a subcritical growth condition.
The property (H) and (Ω) with the exponential representation of holomorphic functions.
The main aim of this paper is to prove that a nuclear Fréchet space E has the property (H) (resp. (Ω)) if and only if every holomorphic function on E (resp. on some dense subspace of E) can be written in the exponential form.
Linear topological invariants of spaces of holomorphic functions in infinite dimension.
It is shown that if E is a Frechet space with the strong dual E* then H(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that H(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished when...
Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime
This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in the two- and three-dimensional quasistatic regimes. CALR associated with negative index materials was discovered by Milton and Nicorovici [21] for constant plasmonic structures in the two-dimensional quasistatic regime. Two key features of this phenomenon are the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others, and the connection between the localized resonance...
Further characterizations of Sobolev spaces
Let be a sequence of non-decreasing functions from into . Under some suitable hypotheses of , we will prove that if , , satisfies , then and moreover , where is a positive constant depending only on and . This extends some results in J. Bourgain and H-M. Nguyen [A new characterization of Sobolev spaces, C. R. Acad Sci. Paris, Ser. 343 (2006) 75-80] and H-M. Nguyen [Some new characterizations of Sobolev spaces, J. Funct. Anal. 237 (2006) 689-720]. We also present some partial results...
Weighted estimates for commutators of multilinear Hausdorff operators on variable exponent Morrey-Herz type spaces
We establish the boundedness for the commutators of multilinear Hausdorff operators on the product of some weighted Morrey-Herz type spaces with variable exponent with their symbols belonging to both Lipschitz space and central BMO space. By these, we generalize and strengthen some previously known results.
Almost-periodic mild solutions to a class of partial functional-differential equations.
Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations.
Local models of the greatest characteristic exponent of differential equations depending on parameters
A simulation of integral and derivative of the solution of a stochastici integral equation
A stochastic integral equation corresponding to a probability space is considered. This equation plays the role of a dynamical system in many problems of stochastic control with the control variable . One constructs stochastic processes , connected with a Markov chain and with the space . The expected values of (i = 1,2) are respectively the expected value of an integral representation of a solution x(t) of the equation and that of its derivative .
A Massera-type criterion for almost periodic solutions of higher-order delay or advance abstract functional differential equations.
A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity
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