We present a description of the diagonal of several spaces in the polydisk. We also generalize some previously known contentions and obtain some new assertions on the diagonal map using maximal functions and vector valued embedding theorems, and integral representations based on finite Blaschke products. All our results were previously known in the unit disk.
Let $\alpha $ be an infinite cardinal. In this paper we define an interpolation rule $\mathop {\mathrm IR}(\alpha )$ for lattice ordered groups. We denote by $C (\alpha )$ the class of all lattice ordered groups satisfying $\mathop {\mathrm IR}(\alpha )$, and prove that $C (\alpha )$ is a radical class.
We extend and generalize some results in local spectral theory for upper triangular operator matrices to upper triangular operator matrices with unbounded entries. Furthermore, we investigate the boundedness of the local resolvent function for operator matrices.
In this review article we present an overview on some a priori estimates in L p , p > 1, recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two L p -bounds, p > 2, for the solution of the associated Dirichlet problem, obtained in correspondence with two different sign assumptions. Then, putting together the above mentioned bounds and using a duality argument, we extend the estimate also to the case 1 < p < 2, for each sign assumption, and for a data in L p ∩ L 2 .
Several constructions of additive generators of binary Archimedean copulas are introduced and discussed. Extension to general Archimedean copulas is also included. Applications to the fitting of copulas to real data are given and examplified.
We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in Cn. Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our proofs are heavily based on nice properties of the r-lattice. Some results of this paper can be also obtained in some unbounded domains, namely tubular domains over symmetric cones., Romi F. Shamoyan, Olivera R. Mihić., and Obsahuje seznam literatury
In the present paper we generalize a few algebraic concepts to graphs. Applying this graph language we solve some problems on subalgebra lattices of unary partial algebras. In this paper three such problems are solved, other will be solved in papers [Pió I], [Pió II], [Pió III], [Pió IV]. More precisely, in the present paper first another proof of the following algebraic result from [Bar1] is given: for two unary partial algebras $\mathbf A$ and $\mathbf B$, their weak subalgebra lattices are isomorphic if and only if their graphs ${\mathbf G}^{\ast }({\mathbf A})$ and ${\mathbf G}^{\ast }({\mathbf B})$ are isomorphic. Secondly, it is shown that for two unary partial algebras $\mathbf A$ and $\mathbf B$ if their digraphs ${\mathbf G}({\mathbf A})$ and ${\mathbf G}({\mathbf B})$ are isomorphic, then their (weak, relative, strong) subalgebra lattices are also isomorphic. Thirdly, we characterize pairs $<{\mathbf L},{\mathbf A}>$, where $\mathbf A$ is a unary partial algebra and $\mathbf L$ is a lattice such that the weak subalgebra lattice of $\mathbf A$ is isomorphic to $\mathbf L$.
Two models of reaction-diffusion are presented: a non-Fickian diffusion model described by a system of a parabolic PDE and a first order ODE, further, porosity-mineralogy changes in porous medium which is modelled by a system consisting of an ODE, a parabolic and an elliptic equation. Existence of weak solutions is shown by the Schauder fixed point theorem combined with the theory of monotone type operators.
For any holomorphic function f on the unit polydisk D n we consider its restriction to the diagonal, i.e., the function in the unit disc D ⊂ C defined by Diag f(z) = f(z, . . . , z), and prove that the diagonal map Diag maps the space Qp,q,s(D n ) of the polydisk onto the space Qbq p,s,n(D ) of the unit disk.