Browsing by Author "BERTOGLIO, N"

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    A REGULARIZATION RESULT OF THE CONTINUOUS PMC MARKOV SEMIGROUPS
    (1991) BERTOGLIO, N; DARTNELL, P; MARTINEZ, S; MARTIN, JS
    Let (W(t))t is-an-element-of R+ be the PMC Markov semigroup and assume usual regular conditions on the probability space (X, Beta, mu). We show that there exist a class of mu-preserving transition kernels (Q(t))t is-an-element-of R+ and a full mu-measure set X approximately such that the action of Q(t) on L2 (mu) is given by W(t), and the semigroup equality Q(t)Q(s)f(x) = Q(t + s)f(x) is verified for any bounded measurable function f, for any x is-an-element-of X approximately and for any t, s is-an-element-of R+.
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    AN ELEMENTARY GEOMETRIC NONSTANDARD PROOF OF THE JORDAN CURVE THEOREM
    (1994) BERTOGLIO, N; CHUAQUI, R
    We give an elementary proof, using nonstandard analysis, of the Jordan curve theorem. We also give a nonstandard generalization of the theorem. The proof is purely geometrical in character, without any use of topological concepts and is based on a discrete finite form of the Jordan theorem, whose proof is purely combinatorial.
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    KICKED DYNAMICS ON HILBERT-SPACES - A NONSTANDARD APPROACH
    (AMER INST PHYSICS, 1995) BERTOGLIO, N; FERNANDEZ, C
    The main purpose of this work is to provide a rigorous interpretation of kicked models, with the aid of nonstandard analysis. These modes are represented by evolution equations involving Dirac's delta functions of time and the method used consists of approximating them by smooth functions on the *R. (C) 1995 American Institute of Physics.
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    MEASURE PRESERVING MARKOV-PROCESSES DENSELY SIMILAR TO ENDOMORPHISMS
    (ELSEVIER SCIENCE BV, 1991) BERTOGLIO, N; MARTINEZ, S
    We characterize the contractions densely similar to the adjoint of some isometry. We deduce a sufficient condition in order to have the evolution of a measure preserving Markov process densely similar to the evolution of an endomorphism on the set of L2-states. This study is in the scope of the reciprocal of the Misra-Prigogine construction in K-systems.
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