Global ETD Search

1	Hankel operators, convolutions and other operators related to linear systems Harper, Zen Michael January 2004 (has links) No description available. 515.7246
2	Hypercyclic operators and related topics Penilla, Manuel De la Rosa Penilla January 2008 (has links) Hypercyclicity, strictly speaking, dates back to 1929 when the first example in the literature appeared. However it was not until the mid-80's, with the discovery of the Hypercyclicity Criterion, that this theory started its evolution. This criterion embraces the conditions that assure a continuous linear operator to be hypercyclic. A considerable number of hypercyclic operators satisfy these conditions. Indeed, every single example known until 2007 satisfied such criterion. It was natural to posed the question if all the hypercyclicity operators must satisfy the Hypercyclicity Criterion, such a question is known as the Great Open Problem in the theory of hypercyclicity. 515.7246
3	The asymptotic stability of stochastic kernel operators Brown, Thomas John 06 1900 (has links) A stochastic operator is a positive linear contraction, P : L1 --+ L1, such that llPfII2 = llfll1 for f > 0. It is called asymptotically stable if the iterates pn f of each density converge in the norm to a fixed density. Pf(x) = f K(x,y)f(y)dy, where K( ·, y) is a density, defines a stochastic kernel operator. A general probabilistic/ deterministic model for biological systems is considered. This leads to the LMT operator P f(x) = Jo - Bx H(Q(>.(x)) - Q(y)) dy, where -H'(x) = h(x) is a density. Several particular examples of cell cycle models are examined. An operator overlaps supports iffor all densities f,g, pn f APng of 0 for some n. If the operator is partially kernel, has a positive invariant density and overlaps supports, it is asymptotically stable. It is found that if h( x) > 0 for x ~ xo ~ 0 and ["'" x"h(x) dx < liminf(Q(A(x))" - Q(x)") for a E (0, 1] lo x-oo then P is asymptotically stable, and an opposite condition implies P is sweeping. Many known results for cell cycle models follow from this. / Mathematical Science / M. Sc. (Mathematics) Markov operator Stochastic operator Asymptotic stability Ergodic theory Biological models Cell cycle models Kernel operations Doubly stochastic operators Harris operators Stochastic process 515.7246 Kernel functions Operator equations -- Asymptotic theory Ergodic theory Cell cycle Stochastic processes Random operators
4	The asymptotic stability of stochastic kernel operators Brown, Thomas John 06 1900 (has links) A stochastic operator is a positive linear contraction, P : L1 --+ L1, such that llPfII2 = llfll1 for f > 0. It is called asymptotically stable if the iterates pn f of each density converge in the norm to a fixed density. Pf(x) = f K(x,y)f(y)dy, where K( ·, y) is a density, defines a stochastic kernel operator. A general probabilistic/ deterministic model for biological systems is considered. This leads to the LMT operator P f(x) = Jo - Bx H(Q(>.(x)) - Q(y)) dy, where -H'(x) = h(x) is a density. Several particular examples of cell cycle models are examined. An operator overlaps supports iffor all densities f,g, pn f APng of 0 for some n. If the operator is partially kernel, has a positive invariant density and overlaps supports, it is asymptotically stable. It is found that if h( x) > 0 for x ~ xo ~ 0 and ["'" x"h(x) dx < liminf(Q(A(x))" - Q(x)") for a E (0, 1] lo x-oo then P is asymptotically stable, and an opposite condition implies P is sweeping. Many known results for cell cycle models follow from this. / Mathematical Science / M. Sc. (Mathematics) Markov operator Stochastic operator Asymptotic stability Ergodic theory Biological models Cell cycle models Kernel operations Doubly stochastic operators Harris operators Stochastic process 515.7246 Kernel functions Operator equations -- Asymptotic theory Ergodic theory Cell cycle Stochastic processes Random operators

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