Baire generic histograms of wavelet coefficients and large deviation formalism in Besov and Sobolev spaces

Wavelet Statistical Models and Besov Spaces

We discover a new relationship between two seemingly diierent image modeling methodologies; the Besov space theory and the wavelet-domain statistical image models. Besov spaces characterize the set of real-world images through a deterministic characterization of the image smoothness, while statistical image models capture the probabilistic properties of images. By establishing a relationship be...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Thermodynamic Formalism, Large Deviation, and Multifractals

On large cardinals and generalized Baire spaces

Working under large cardinal assumptions, we study the Borel-reducibility between equivalence relations modulo restrictions of the non-stationary ideal on some fixed cardinal κ. We show the consistency of E ++,λ++ λ-club , the relation of equivalence modulo the non-stationary ideal restricted to Sλ ++ λ in the space (λ++)λ ++ , being continuously reducible to E ++ λ+-club , the relation of equi...

Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains

Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of developing a similar sharp theory for semilinear problems of the type ∆u − N(x, u) = F (x), equipped with Dirichlet and Neumann boundary conditions.