Zeta functions and transfer operators for piecewise monotone transformations
نویسندگان
چکیده
منابع مشابه
Dynamical Zeta Functions and Transfer Operators, Volume 49, Number 8
C ertain generating functions—encoding properties of objects like prime numbers, periodic orbits, ...—have received the name of zeta functions. They are useful in studying the statistical properties of the objects in question. Zeta functions have generally been associated with problems of arithmetic or algebra and tend to have common features: meromorphy, Euler product formula, functional equat...
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We evaluate zeta-functions ζ(s) at s = 0 for invariant non-minimal 2nd-order vector and tensor operators defined on maximally symmetric even dimensional spaces. We decompose the operators into their irreducible parts and obtain their corresponding eigenvalues. Using these eigenvalues, we are able to explicitly calculate ζ(0) for the cases of Euclidean spaces and N -spheres. In the N -sphere cas...
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We describe a general method to prove meromorphic continuation of dynamical zeta functions to the entire complex plane under the condition that the corresponding partition functions are given via a dynamical trace formula from a family of transfer operators. Further we give general conditions for the partition functions associated with general spin chains to be of this type and provide various ...
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We study a question posed by Stephen Simons in his 2008 monograph involving “bigger conjugate” (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the state-of-the-art of harder problems in monotone operator theory, especially the sum problem. In this paper, we provide some tools fo...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1990
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf02104498