Related papers: Two infinite versions of nonlinear Dvoretzky's the…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is…
We construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems. The symmetries in question generalize those found by Chen,…
In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…
This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the…
We give a general approach to infinite dimensional non-Gaussian Analysis for measures which need not have a logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.
Littlewood's theorem is one of the pioneering results in random analytic functions over the open unit disk. In this paper, we prove some analogues of this theorem for Hardy spaces in infinitely many variables. Our results not only cover…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
We prove a number of results concerning the Hausdorff and packing dimension of sets of points which escape (at least in average) to infinity at a given rate under non-autonomous iteration of exponential maps. In particular, we generalize…
We show that the set of numbers that are $Q$-distribution normal but not simply $Q$-ratio normal has full Hausdorff dimension. It is further shown under some conditions that countable intersections of sets of this form still have full…
We consider the properties of massive one particle states on a translation covariant Haag-Kastler net in Minkowski space. In two dimensional theories, these states can be interpreted as soliton states and we are interested in the existence…
We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in the whole space or in any cylindrical smooth domain with smooth boundary data one can find an…
We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An…
Some results of B. Pasynkov and H. Torunczyk on finite-dimensional maps are improved. A generalization of a Dranishnikov-Uspenskij theorem about extensional dimension is also obtained.
By means of the Ehrenfest's Theorem inside the context of a noncommutative Quantum Mechanics it is obtained the Newton's Second Law in noncommutative space. Considering discrete systems with infinite degrees of freedom whose dynamical…
The Hausdorff-Alexandroff Theorem states that any compact metric space is the continuous image of Cantor's ternary set $C$. It is well known that there are compact Hausdorff spaces of cardinality equal to that of $C$ that are not continuous…
Given a compact of ${\bf R}^n$, there is always a doubling measure having it as its support. We use this fact to construct an integral operator that extends differentiable functions defined on any compact set of ${\bf R}^n$ to the whole of…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
We study a class of semilinear diffusion equations on infinite, connected, weighted graphs, focusing on two types of nonlinearities: monotone decreasing and Lipschitz continuous. Under minimal structural assumptions on the graph, we…
The aim of this paper is to study ultralimits of pointed metric measure spaces (possibly unbounded and having infinite mass). We prove that ultralimits exist under mild assumptions and are consistent with the pointed measured…