We consider the norm convergence for a special matrix-based de la Vallée Poussin-like mean of Fourier series with respect to the Vilenkin system. We estimate the difference between the named mean above and the corresponding function in norm, and the upper estimation is given by the modulus of continuity of the function. We also give theorems with respect to norm and almost everywhere convergences.
In this paper, we continue to consider the value cross-sharing problems on meromorphic functions. We mainly present some results and improvements on (f(z)) and (g(z)) provided that (f(z)) and (g^{(k)}(z)) share common values together with (g(z)) and (f^{(k)}(z)) share the same or different common values CM or IM, where (f(z), g(z)) are meromorphic functions and (k) is a positive integer. With additional conditions on deficiency, we get more accurate relations on (f(z)) and (g(z)) when (f(z)) and (g^{(k)}(z)) share a CM together with (g(z)) and (f^{(k)}(z)) share b CM, where a, b are constants.
We study a distance graph (Gamma_n) that is isomorphic to the (1)-skeleton of an (n)-dimensional unit hypercube. We show that every measurable set of positive upper Banach density in the plane contains all sufficiently large dilates of (Gamma_n). This provides the first examples of distance graphs other than the trees for which a dimensionally sharp embedding in positive density sets is known.
The notion of decomposable operators acting between distinct (L^p)-direct integrals of Banach spaces is introduced. We show that these operators generalize the composition operator in the sense that a binary relation replaces a mapping. The necessary and sufficient conditions for the boundedness of those operators are the main results of the paper.
Motivated by [19] and [10], we define the modified proximity function (overline{m}_{q}(f,r)) for entire curves in complex projective space (mathbf{P}^nmathbf{C}), and establish an asymptotic equality of Cartan's Second Main Theorem. This is a generalization of [19, Theorem 1.6] for transcendental meromorphic functions. Moreover, we strengthen the result to entire curves of finite order and holomorphic mappings over multiple variables.
For the polar derivative (D_alpha P(z) =nP(z)+(alpha-z)P'(z)) of a polynomial (P(z)) of degree n, most of the (L^p) inequalities available in the literature are for restricted values of (alpha), and in this paper we extend few such fundamental results to all of (alpha) in the complex plane.
We show that the composition hyperbolic group in the unit disc, once transferred to act on sequence spaces, is bounded on (ell^p) if and only if ({p=2}). We introduce some integral operators subordinated to that group which are natural generalizations of classical operators on sequences. For the description of such operators, we use some combinatorial identities which look interesting in their own.
In this paper, we study the strong extension groups of Cuntz–Krieger algebras, and present a formula to compute the groups. We also detect the position of the Toeplitz extension of a Cuntz–Krieger algebra in the strong extension group and in the weak extension group to see that the weak extension group with the position of the Toeplitz extension is a complete invariant of the isomorphism class of the Cuntz–Krieger algebra associated with its transposed matrix.
Each symmetrically-normed ideal (mathcal{I}) of compact operators on a Hilbert space (H) induces a multiplier topology (mu^*_{mathcal{I}}) on the algebra (mathcal{B}(H)) of bounded operators. We show that under fairly reasonable circumstances those topologies precisely reflect, strength-wise, the inclusion relations between the corresponding ideals, including the fact that the topologies are distinct when the ideals are.
Said circumstances apply, for instance, for the two-parameter chain of Lorentz ideals (mathcal{L}^{p,q}) interpolating between the ideals of trace-class and compact operators. This gives a totally ordered chain of distinct topologies (mu^*_{p,qmid 0}) on (mathcal{B}(H)), with (mu^*_{2,2mid 0}) being the (sigma mbox{-}strong^*) topology and (mu^*_{infty,inftymid 0}) the strict/Mackey topology. In particular, the latter are only two of a natural continuous family.
We generalize a fundamental theorem on positive matrix semigroups stating that each component is either strictly positive for all times or identically zero (“Lévy’s Theorem”). Our proof of this fact that does not require the matrices to be continuous at time zero. We also provide a formulation of this theorem in the terminology of positive operator semigroups on sequence spaces.
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：