1,721,033 research outputs found
Schauder theorems for a class of (pseudo-)differential operators on finite- and infinite-dimensional state spaces
No full textLunardi A, Röckner M. Schauder theorems for a class of (pseudo-)differential operators on finite- and infinite-dimensional state spaces. Journal of the London Mathematical Society . 2021;104(2):492-540.We prove maximal regularity results in Holder and Zygmund spaces for linear stationary and evolution equations driven by a class of differential and pseudo-differential operators L, both in finite and in infinite dimension. The assumptions are given in terms of the semigroup generated by L. We cover the cases of fractional Laplacians and Ornstein-Uhlenbeck operators with fractional diffusion in finite dimension, and several types of local and nonlocal Ornstein-Uhlenbeck operators, as well as the Gross Laplacian and its fractional powers, in infinite dimension
Ornstein-Uhlenbeck semigroups in infinite dimension
No full textThis is a survey paper about Ornstein-Uhlenbeck semigroups in infinite dimension and their generators. We start from the classical Ornstein-Uhlenbeck semigroup on Wiener spaces and then discuss the general case in Hilbert spaces. Finally, we present some results for Ornstein-Uhlenbeck semigroups on Banach spaces. This article is part of the theme issue 'Semigroup applications everywhere'
Time regularity for generalized Mehler semigroups
No full textWe study continuity and Holder continuity of t bar right arrow P(t)f, where P-t is a generalized Mehler semigroup in C-b(X), the space of the continuous and bounded functions from a Banach space X to R, and f is an element of C-b(X). The generators L of such semigroups are realizations of a class of differential and pseudo-differential operators, both in finite and in infinite dimension. Examples of operators L to which this theory is applicable include Ornstein-Uhlenbeck operators with fractional diffusion in finite dimension, and Ornstein-Uhlenbeck operators with associated strong-Feller semigroups, in infinite dimension
Interpolation Between Spaces of Continuous Functions
No full textWe characterize some interpolation spaces between spaces of continuous functions in a bounded open set ω ⊂ IRn and domains of elliptic operators with Dirichlet or mixed boundary condition. © 1985, Elsevier Inc. All rights reserved
Tipologia, uso e materie prime delle industrie in pietra non scheggiata della Cultura dei VBQ: materiali dal Veneto e dalla Liguria a confronto
No full textThis work presents the results of a comparative study of polished and ground stone tools from
two geographical areas of the Square-Mouthed Pottery Culture (Middle Neolithic): Liguria and in particular the
assemblage from Arene Candide (617 pieces) and 3 sites of the Veneto region namely Fimon-Molino Casarotto,
Quinzano and Rivoli-Rocca (all together 237 pieces). Terminological questions, raw materials and their procurement
strategy, operative chain and functional aspects have been considered to reach a terminology which can be shared
among scholars. The method of the study included the identification of the raw materials and their textural
characteristics, the macroscopic observation of the use wears, the experimental reproduction of instruments for
the techno-functional operative chains reconstruction. From the comparative study of the instruments of the two
different regions, some common characteristics emerged, which can be considered peculiar of the chronological and
cultural context. They can be summarized as follows: the use of different variety of local lithologies (limestones,
sandstones, porphyry) for all the instruments excepting cutting edged tools, such as axes/adzes and chisels, which
have been always manufactured from HP-metaophiolites, imported from the western Alpine sources. From the
technological point of view, a complex operative chain involving the shaping and reworking of the working surfaces
was enlightened. From the functional point of view, the assemblages include a wide variety of tools, such as axes,
adzes, chisels, grinding stones, millstones, hammer stones, pestles and burnishers. The use wear analysis and the
comparative study with the experimental replicas permitted to identify different activities and functional categories
and to reconstruct the nature of the different materials (cereals, wood, minerals, leather etc.) processed and worked
with the tools. A further achievement was to recognize the existence of multifunctional instruments and the recycling
of some tools, which testify for the complexity of the use-reuse-discard cycle of the raw materials. To conclude, the
results of the study showed that this category of artefacts can be considered as markers of specific economical and
artisanal activities performed at the different sites
Smoothing of quasilinear parabolic operators and applications to forward-backward stochastic systems
No full textSchauder theorems for Ornstein-Uhlenbeck equations in infinite dimension
No full textWe prove Schauder type estimates for stationary and evolution equations driven by the classical Ornstein-Uhlenbeck operator in a separable Banach space, endowed with a centered Gaussian measure
BV functions in Hilbert spaces
No full textWe study the basic theory of BV functions in a Hilbert space X endowed with a (not necessarily Gaussian) probability measure ν. We present necessary and sufficient conditions in order that a function u∈ Lp(X, ν) is of bounded variation. We also discuss the De Giorgi approach to BV functions through the behavior as t→ 0 of ∫X‖∇T(t)u‖dν, for a smoothing semigroup T(t). Particular attention is devoted to the case where u is the indicator function of a sublevel set {x:g(x
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