Titlebook: Analysis on Lie Groups with Polynomial Growth; Nick Dungey,A. F. M. Elst,Derek W. Robinson Textbook 2003 Birkh?user Boston 2003 Algebraic

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Deyuan Meng,Mingjun Du,Yuxin Wuheavily on the Lie group formulation of homogenization theory given in Chapter IV and uses the Gaussian bounds of Theorem IV.7.1. The derivation of the latter bounds relied implicitly on homogenization but in the asymptotics the homogenized operator and the corresponding semigroup and kernel play an

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0743-1643 s well as researchers in the above areas. Prerequisites include knowledge of basic results from semigroup theory and Lie group theory..978-1-4612-7399-8978-1-4612-2062-6Series ISSN 0743-1643 Series E-ISSN 2296-505X

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Asymptotics,p .. ?.and its kernel 11 ?.on the group .., where.is the semigroup generated by the homogenized operator.on ..(..) and .. = .. . .. (.) is the projection onto the constant functions on .. In fact one can identify the first-order corrections in an asymptotic expansion and obtain estimates on the rate

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Introduction,mplest constraint resulting from the group action is on the volume growth. There are only two possibilities. In the first case the volume of a ball grows no faster than a power of its radius. Groups with this characteristic are called Lie groups of polynomial growth. Compact Lie groups fall within t

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General Formalism,hich are summarized for later reference. A second part consists of the basic definitions of subelliptic operators and the related semigroups together with the description of some preliminary results which motivate the later analysis. Thirdly, we introduce several techniques adapted to the Lie group

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Asymptotics,heavily on the Lie group formulation of homogenization theory given in Chapter IV and uses the Gaussian bounds of Theorem IV.7.1. The derivation of the latter bounds relied implicitly on homogenization but in the asymptotics the homogenized operator and the corresponding semigroup and kernel play an

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General Formalism,analysis. Since most of the reference material is quite standard it is summarized in formal statements without proof. Further details and specific references to the literature are, however, given in the Notes and Remarks at the end of the chapter.