Infinite systems of functions
نویسندگان
چکیده
منابع مشابه
Entropy of infinite systems and transformations
The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...
متن کاملTransfer functions for infinite-dimensional systems
where A is the infinitesimal generator of the C0-semigroup T (t) on the state space X, B is a bounded linear operator from input space U to X, C is a bounded linear operator from X to the output space Y , and D is a bounded operator from U to Y . The spaces X, U and Y are assumed to be Banach spaces. More detail on the system (1) can be found in Curtain and Zwart [1]. For the system (1) we intr...
متن کاملNonanalyticities of entropy functions of finite and infinite systems.
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems. The relation between finite and infinite system nonanalyticities is illustrated by means of a simple classical spinlike model which is exactly solvable for both finite and infinite system sizes, showing a phas...
متن کاملGreen's Functions for Linear Differential Systems of Infinite Order.
probability 1. (Note that we do not assume any relation of dependence or indepenaence between X(r) and X(s) for m $ n.) 1 See M. Frechet, Recherches theoriques modernes, Vol. 1, Paris, 1937, p. 27. 2 See H. Cram&r, Mathematical methods of statistics, Princeton, 1946, p. 93. Compare F. P. Cantelli, Considerazioni sulla legge uniforme dei grandi numeri ecc., Giornale dell 'Istituto Italiano degli...
متن کاملRandom Walks on Infinite Free Products and Infinite Algebraic Systems of Generating Functions
The return probabilities of certain random walks on infinite free products of finite groups are shown to obey a Local Limit Theorem of the same type as for nearestneighbor random walks on finite free products. The analysis is based on an infinitedimensional extension of a technique for studying finite algebraic systems of generating functions introduced by the author in [12] and [13].
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1920
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1920-03308-2