Markov chains as Evans-Hudson diffusions in Fock space
Markov Chains, Riesz Transforms and Lipschitz Maps.
Markov convexity and local rigidity of distorted metrics
It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type if and only if it is Markov -convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric spaces, showing in particular that tree metrics fail to have the dichotomy property.
Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory
Markov operators on the space of vector measures; coloured fractals
We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.
Markov traces on universal Jones algebras and subfactors of finite index.
Markovian processes on mutually commuting von Neumann algebras
The aim of this paper is to study markovianity for states on von Neumann algebras generated by the union of (not necessarily commutative) von Neumann subagebras which commute with each other. This study has been already begun in [2] using several a priori different notions of noncommutative markovianity. In this paper we assume to deal with the particular case of states which define odd stochastic couplings (as developed in [3]) for all couples of von Neumann algebras involved. In this situation...
Martin boundary theory of some quantum random walks
Martingale convergence theorems in -algebras.
Martingale inequalities in exponential Orlicz spaces.
Martingale operators and Hardy spaces generated by them
Martingale Hardy spaces and BMO spaces generated by an operator T are investigated. An atomic decomposition of the space is given if the operator T is predictable. We generalize the John-Nirenberg theorem, namely, we prove that the spaces generated by an operator T are all equivalent. The sharp operator is also considered and it is verified that the norm of the sharp operator is equivalent to the norm. The interpolation spaces between the Hardy and BMO spaces are identified by the real method....
Martingales, G...-Embeddings and Quotients of L1 .
Martingales in Banach *-algebras.
Mathematical analysis for the peridynamic nonlocal continuum theory
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
Mathematical analysis for the peridynamic nonlocal continuum theory*
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
Mathematical and Computational Models in Tumor Immunology
The immune system is able to protect the host from tumor onset, and immune deficiencies are accompanied by an increased risk of cancer. Immunology is one of the fields in biology where the role of computational and mathematical modeling and analysis were recognized the earliest, beginning from 60s of the last century. We introduce the two most common methods in simulating the competition among the immune system, cancers and tumor immunology strategies:...
Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation, we...
Matrices of positive polynomials.
Matrix subspaces of L₁
If and are two 1-unconditional basic sequences in L₁ with E r-concave and F p-convex, for some 1 ≤ r < p ≤ 2, then the space of matrices with norm embeds into L₁. This generalizes a recent result of Prochno and Schütt.
Matrix transformations and almost convergence