相关论文: On the Representation of Holomorphic Functions on …
We show the completeness of the system of generalized eigenfunctions of closed extensions of elliptic cone operators under suitable conditions on the symbols.
We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.
In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J.…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
We discuss the polar in symbol space to hypoelliptic and partially hypoelliptic operators, assuming a transmission property related to a rectifiable boundary and using a representation based on two scalar products.
The present paper deals with a generalization of the Baskakov operators. Some direct theorems, asymptotic formula and $A$-statistical convergence are established. Our results are based on a $\rho$ function. These results include the…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…
We investigate the boundary behavior of holomorphic functions with respect to a family of curves in a domain of finite type. This work is a generalization of \u{C}irka's classical result on the unit ball and it supplements the result by…
Interrelation of the Coleman's representabilty theory for 1-density operators and abstract algebraic form of the Hohenberg-Kohn theorem is studied in detail. Convenient realization of the Hohenberg-Kohn set of classes of 1-electron…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…
This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R^n, n > 1. The theory of pseudodifferential boundary problems has turned out to be very…
It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…
In this paper, we will give an extension of Mok's theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.
We establish an operator extension of the following generalization of Bohr's inequality, due to M.P. Vasi\'c and D.J. Ke\v{c}ki\'{c}: $$|\sum_{i=1}^n z_i|^r \leq (\sum_{i=1}^n \alpha_i^{1/(1-r)})^{r-1}\sum_{i=1}^n \alpha_i|z_i|^r \quad…
We show how eigenvalue estimates for linear operators can be used to obtain new Blaschke type bounds on zeros of holomorphic functions on the unit disk.
Let $X, Y$ be two complex manifolds, let $D\subset X,$ $ G\subset Y$ be two nonempty open sets, let $A$ (resp. $B$) be an open subset of $\partial D$ (resp. $\partial G$), and let $W$ be the 2-fold cross $((D\cup A)\times B)\cup…