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Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields
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Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions
We investigate several topics related to the local behavior of functions: pointwise Hölder regularity, local scaling invariance and very oscillatory "chirp-like" behaviors. Our main tool is to relate these notions to two-microlocal conditions which are defined either on the Littlewood-Paley decomposition or on the wavelet transform. We give characterizations and the main properties of these two-microlocal spaces and we give several applications, such as bounds on the dimension of the set of Hölder singularities of a function, Sobolev regularity of trace functions, and chirp expansions of specific functions.
Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains
In Chapter I, various (numerical) semigroup-theoretic concepts and constructions are introduced and characterized. Applications in Chapter II are made to the study of Noetherian local one-dimensional analytically irreducible integral domains, especially for the Gorenstein, maximal embedding dimension, and Arf cases, as well as to the so-called Kunz case, a pervasive kind of domain of Cohen-Macaulay type 2.
The Index Theorem for Minimal Surfaces of Higher Genus
In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.
On the Martingale Problem for Interactive Measure-Valued Branching Diffusions
This book develops stochastic integration with respect to ``Brownian trees'' and its associated stochastic calculus, with the aim of proving pathwise existence and uniqueness in a stochastic equation driven by a historical Brownian motion. Perkins uses these results and a Girsanov-type theorem to prove that the martingale problem for the historical process associated with a wide class of interactive branching measure-valued diffusions (superprocesses) is well-posed. The resulting measure-valued processes will arise as limits of the empirical measures of branching particle systems in which particles interact through their spatial motions or, to a lesser extent, through their branching rates.
Random Perturbations of Hamiltonian Systems
Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.
Generalized Tate Cohomology
Let [italic capital]G be a compact Lie group, [italic capitals]EG a contractible free [italic capital]G-space and let [italic capitals]E~G be the unreduced suspension of [italic capitals]EG with one of the cone points as basepoint. Let [italic]k*[over][subscript italic capital]G be a [italic capital]G-spectrum. Let [italic capital]X+ denote the disjoint union of [italic capital]X and a [italic capital]G-fixed basepoint. Define the [italic capital]G-spectra [italic]f([italic]k*[over][subscript italic capital]G) = [italic]k*[over][subscript italic capital]G [up arrowhead symbol] [italic capitals]EG+, [italic]c([italic]k*[over][subscript italic capital]G) = [italic capital]F([italic capitals]EG...
Brownian Motion on Nested Fractals
Lindstrom (U. of Oslo) constructs Brownian motion on a reasonably general class of self-similar fractals. He deals with diffusions, self-similar fractals, fractal Laplacians, asymptotic distribution of eigenvalues, nonstandard analysis. Annotation copyright Book News, Inc. Portland, Or.
Lebesgue Theory in the Bidual of C(X)
The present work is based upon our monograph "The Bidual of [italic capital]C([italic capital]X)" ([italic capital]X being compact). We generalize to the bidual the theory of Lebesgue integration, with respect to Radon measures on [italic capital]X, of bounded functions. The bidual of [italic capital]C([italic capital]X) contains this space of bounded functions, but is much more 'spacious', so the body of results can be expected to be richer. Finally, we show that by projection onto the space of bounded functions, the standard theory is obtained.
Tilting in Abelian Categories and Quasitilted Algebras
We generalize tilting with respect to a tilting module of projective dimension at most one for an Artin algebra to tilting with respect to a torsion pair in an Abelian category. Our construction is motivated by the connection between tilting and derived categories. We develop a general theory for such tilting, and are led to a generalization of tilting algebras which we call quasitilted algebras. This class also contains the canonical algebras, and we show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. We also give other characterizations of quasitilted algebras, and give methods for constructing such algebras.
