On m-rectangle characteristics and isomorphisms of mixed (F)-, (DF)-spaces

In this thesis, we consider problems on the isomorphic classification and quasiequivalence properties of mixed (F)-, (DF)- power series spaces which, up to isomorphisms, consist of basis subspaces of the complete projective tensor products of power series spaces and (DF)- power series spaces. Important linear topological invariants in this consideration are the m-rectangle characteristics, which compute the number of points of the de ning sequences of the mixed (F)-, (DF)- power series spaces, that are inside the union of m rectangles. We show that the systems of m-rectangle characteristics give a complete characterization of the quasidiagonal isomorphisms between Montel spaces that are in certain classes of mixed (F)-, (DF)- power series spaces under proper de nitions of equivalence. Using compound invariants, we also show that the m-rectangle characteristics are linear topological invariants on the class of mixed (F)-, (DF)- power series spaces that consist of basis subspaces of the complete projective tensor products of a power series space of nite type and a (DF)- power series space of in nite type. From these invariances, we obtain the quasiequivalence of absolute bases in the spaces of the same class that are Montel and quasidiagonally isomorphic to their Cartesian square

On isomorphisms of spaces of analytic functions of several complex variables

In this thesis, we discuss results on isomorphisms of spaces of analytic functions of several complex variables in terms of pluripotential theoretic considerations. More specifically, we present the following result: Theorem 1 Let Ω be a Stein manifold of dimension n. Then, A(Ω) ≈ A(U[n]) if and only if Ω is pluriregular and consists of at most finite number of connected components. The problem of isomorphic classification of spaces of analytic functions is also closely related to the problem of existence and construction of bases in such spaces. The essential tools we use in our approach are Hilbert methods and the interpolation properties of spaces of analytic functions which give us estimates of dual norms and help us to obtain extendable bases for pluriregular pairs

Fitted Q-Learning in Mean-field Games

In the literature, existence of equilibria for discrete-time mean field games has been in general established via Kakutani's Fixed Point Theorem. However, this fixed point theorem does not entail any iterative scheme for computing equilibria. In this paper, we first propose a Q-iteration algorithm to compute equilibria for mean-field games with known model using Banach Fixed Point Theorem. Then, we generalize this algorithm to model-free setting using fitted Q-iteration algorithm and establish the probabilistic convergence of the proposed iteration. Then, using the output of this learning algorithm, we construct an approximate Nash equilibrium for finite-agent stochastic game with mean-field interaction between agents.Comment: 22 page

Frequently hypercyclic weighted backward shifts on spaces of real analytic functions

We study frequent hypercyclicity in the case of weighted backward shift operators acting on locally convex spaces of real analytic functions. We obtain certain conditions on frequent hypercyclicity and linear chaoticity of these operators using dynamical transference principles and the frequent hypercyclicity criterion.Publisher versio

Eigenvalues and dynamical properties of weighted backward shifts on the space of real analytic functions

Usually backward shift is neither chaotic nor hypercyclic. We will show that on the space A(Omega) of real analytic functions on a connected set Omega subset of R with 0 is an element of Omega, the backward shift operator is chaotic and sequentially hypercyclic. We give criteria for chaos and for many other dynamical properties for weighted backward shifts on A(Omega). For special classes of them we give full characterizations. We describe the point spectrum and eigenspaces of weighted backward shifts on A(Omega) as above.National Center of Science (Poland) ; TÜBİTA