Related papers: A Rado theorem for complex spaces
In this paper, we will generalize the definition of partially random or complex reals, and then show the duality of random and complex, i.e., a generalized version of Levin-Schnorr's theorem. We also study randomness from the view point of…
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and study some of their properties. In particular we obtain a support theorem that generalizes Helgason's support theorem for…
We generalize Jacod's condition and introduce a new type sufficient condition for the uniform integrability of the general stochastic exponential.
We give a geometric proof of the Routh's theorem for tetrahedra.
In this paper, we present a novel generalization of the classical Ceva theorem to arbitrarily dimensional simplexes. Our approach allows cevians to have any dimension (smaller than the dimension of the base simplex). Consequently, our…
In the paper, we generalize the Arzel\`a-Ascoli theorem in the setting of uniform spaces. At first, we recall well-known facts and theorems coming from monographs of Kelley and Willard. The main part of the paper introduces the notion of…
In this note, we prove an $L^2$ Hartogs-type extension theorem for unbounded domains.
We present a method to compute the holonomic extension of a $D$-module from a Zariski open set in affine space to the whole space. A particular application is the localization of coherent $D$-modules which are holonomic on the complement of…
We prove a connectedness result for products of weighted projective spaces.
We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain…
We generalize several classical theorems in extremal combinatorics by replacing a global constraint with an inequality which holds for all objects in a given class. In particular we obtain generalizations of Tur\'an's theorem, the…
We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.
The following theorem is proved: Let M be a locally Lipschitz hypersurface in C^n with one-sided extension property at each point (e.g., without analytic discs). Let S be a closed subset of M and f : M \ S ---> C^m \ E is a CR-mapping of…
In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…
By using nonstandard analysis, and in particular iterated hyper-extensions, we give foundations to a peculiar way of manipulating ultrafilters on the natural numbers and their pseudo-sums. The resulting formalism is suitable for…
In this note, we answer a question on the extension of $L^{2}$ holomorphic functions posed by Ohsawa.
We study the weighted Fock spaces in one and several complex variables. We evaluate the dimension of these spaces in terms of the weight function extending and completing earlier results by Rozenblum-Shirokov and Shigekawa.
A tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.
We amalgamate two generalizations of Ramsey's Theorem--Ramsey classes and the Erd\H{o}s-Rado Theorem--into the notion of a combinatorial Erd\H{o}s-Rado class. These classes are closely related to Erd\H{o}s-Rado classes, which are those from…