In this paper, utilizing the method of operator theory, some properties and perturbation of g-franes in Hilbert C*-modules are discussed. some characterizations of sums of g-frames in Hilbert C*-modules are obtained. Moreover, it is shown that these results extend and improve the existing results.
Through the establishment of a new space, we prove an embedding theorem. Furthermore, using that embedding theorem and mountain pass theorem, we obtain the existence of nontrivial solutions of a biharmonic problem in the new space.
Based on a 2 × 2 spectral problem, the corresponding hierarchy of evolution equations is derived. According to the property of its 2 × 2 Lenard pair of operators, it can be checked that the hierarchy is a generalized Hamilton system and possesses Bi-Hamilton structure and Multi-Hamilton structure. Furthermore, its Liouville integrability is also evidenced. What's more, this hierarchy, in special cases, can reduce to the general TD hierarchy, TD hierarchy, general C-KdV hierarchy, C-KdV hierarchy, etc. In the end, the one to one relation between the Hamilton functionals and the conservation densities are provided too.
A vector-valued Ekeland's variational principle is introduced, where the objective function is from a complete metric space into a cone-ordered topological linear space. This result is a generalization of the Ekeland's variational principle obtained by Zhong Chengkui.
In this paper, the existence, uniqueness and decay properties for the strong solutions of the MHD equations in spacePLn∩PLp, (1<p<n,n≥2) are studied by applying the semi-group theory and the method used by Kato[1].
Let X and Y be Banach spaces, A∈B(X),B∈B(Y), C∈B(Y,X), MC=(A0CB) be the operator matrix acting on the Banach space X⊕Y. In this paper, we give out 20 kind spectra structure of MC, decide 18 kind spectra filling-in-hole properties of MC and present some interesting examples of these problems.
The model of age-independent branching processes with static immigration in random environments is introduced. Giving the renewal equation of conditional generation function and considering the Kolmogorov equation for the special case. Moreover, we obtain the moments through studying the renewal equation and consider the extinction probability simply. Finally, we give an open problem.
Let f(z)=h(z)+g(z) be a harmonic mapping of the unit disk U. In this paper, the sharp coefficient estimates for bounded planar harmonic mappings are established, the sharp coefficient estimates for normalized planar harmonic mappings with |h(z)|+|g(z)|≤M are also provided. As their applications, Landau's theorems for certain biharmonic mappings are provided, which improve and refine the related results of earlier authors.
The authors prove that the commutators of Multipliers not only has the (Mpq(Rn), Lip(β-(n/q))(Rn)) boundedness but also has the (Mpq(Rn), BMO(Rn)) boundedness. Furthermore, the boundedness of Multipliers and commutators on the generalized Morrey space Lp,ρ(Rn) is established.
First of all, the necessary and sufficient conditions concerning the exponential stability of degenerate C0-semigroup are obtained via functional analysis and operator theory in Hilbert space. Then, the exponential stability for a family of degenerate C0-semigroup is discussed, the necessary and sufficient conditions are given in the light of degenerate C0-semigroup.
Let Ω be a function on the unit sphere and b a radial function, and ρ be a complex parameter with Re (ρ)>0. Let Ψ be in C2([0,∞)), convex, and increasing function with Ψ(0) = 0. The parametric Marcinkiewicz operator μρΩ, b with nonhomogenous rough kernel and the rough Marcinkiewicz operator μρΩ, Ψ, b related to a surface of revolutions are considered in this paper, we prove the boundedness of these Marcinkiewicz operators on Hardy spaces and weak Hardy spaces under the minimum smooth conditions for the rough kernels Ω and b. The results in this paper extend as well as improve previously known results.
Let a be a positive integer with a>1, f(a) be a polynomial of a with nonnegative integer coefficients, and f(1)=2rp+4, where r is a positive integer with r>1, p=2l-1 is a Mersenne prime. In this paper, the finiteness of positive integer solution (x,n) of the equation
(a-1)x2+f(a)=4an
is discussed, and prove that if f(a)=91a+9, then the equation has only the positive integer solutions (x,n)=(3,3), (11,3) and (3,4) for a=5,7 and 25 respectively.
We prove a generalized Ul'yanov type inequality for the classical moduli of smoothness on the unit sphere, which has important applications in imbedding theory, spherical polynomial approximation and the theory of interpolation in function spaces on the sphere. Our proof is based on several new estimates on spherical harmonic expansions, which seem to be of independent interest.
We have classified completely the space-like hypersurfaces with parallel conformal second fundamental forms in the conformal space. In this work, we study the time-like case and classify the Type I time-like hypersurfaces with parallel conformal second fundamental forms.
In this paper we introduce the concept and operations of the function system matrix, contruct the complete family of fractals by the function system matrix, and we determine the Hausdorff dimension and the Box-dimension of the complete family of similar fractals under the open set conditions.
The analytical characteristics of a class of fractal interpolation functions (FIFs) with function vertical scaling factors, including smoothness, stability and sensitivity, are studied in this work. The results on smoothness of such FIFs are presented, and their stability is proved. In addition, the sensitivity and moments for the class of FIFs are discussed. It is shown that if a small perturbation occurs in the iterated function systems (IFSs) generating the class of FIFs, then a small perturbation is also produced in the corresponding FIFs and their moments. The upper estimates of the perturbation errors are given.
In this paper, firstly we give a condition for two semi-frame sequences such that both of them be frames for Hilbert space H, which is related to the perturbation theory of frames. Then we give some conditions on dilation and translation parameters and the generating functions such that wavelet frames for L2(R) are generated. These results generalize the classical similar results in literatures. We also discuss the Bessel sequence and add some other sufficient conditions.
The unitary equivalence of multiplication operator Mφ on the Dirichlet space D is studied, where φ is a Blaschke product of order two. The main result shows that for a multiplier ψ of D, the multiplication operator Mψ is unitarily equivalent to Mφ if and only if ψ(z)=φ(θz) for some constant θ with |θ|=1. This is very different from the corresponding result in the Hardy space and in the Bergman space.
