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Some Constructions in the Inverse Spectral Theory of Cyclic Groups

BEN GREEN
2003 Combinatorics, probability & computing  
We show that a recent result of Chang concerning the structure of the large spectrum is best possible. Chang's result has already found a number of applications in combinatorial number theory.  ...  The results of this paper concern the "large spectra" of sets, by which we mean the set of points in F × p at which the Fourier transform of a characteristic function χ A , A ⊆ F p , can be large.  ...  in which so-called niveau sets are constructed.  ... 
doi:10.1017/s0963548302005436 fatcat:23jq3ifzhrcwrmxrncllzgry7u

Rational algebraic $K$-theory of certain truncated polynomial rings

R. E. Staffeldt
1985 Proceedings of the American Mathematical Society  
Our method is homological calculation which is facilitated by some basic rational homotopy theory and interpreted in terms of the cyclic homology theory of algebras invented by Alain Connes.  ...  In §2 of this paper we sketch a computation in cyclic homology relevant to the case A = 0[T]/(T" + 1) following the steps of a computation of the rational algebraic ^-theory of the space CP" shown to us  ...  We here adopt the plus-construction definition of algebraic A"-theory and study the spectral sequences of the fibrations of classifying spaces associated to the exact sequences of groups 1 ^ G"a) -GL"(  ... 
doi:10.1090/s0002-9939-1985-0801322-4 fatcat:kaihmk6qarbpvagdigiqlsfibq

Page 331 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
331 46L itive map o,,,, implemented by a finite basis {x;} of the Hilbert bimodule so that they show the existence of KMS-states at inverse temperatures equal to the logarithms of the spectral radii of  ...  Then they define Chern characters from K-theory to en- tire cyclic homology of compact quantum groups and show that the Chern characters in both the topological and algebraic cases are isomorphisms modulo  ... 

Page 639 of Mathematical Reviews Vol. 50, Issue 3 [page]

1975 Mathematical Reviews  
In fact, for each prime p23, and for an arbitrary field F of char p, he constructs a cyclic permanent group <A,) of order 2p con- sisting of px p matrices over F such that A, does not have the 1-diagonal  ...  Conditions for an irreducible stochastic matrix to have a stochastic spectral inverse. Further, we give some partial results concerning the general stochastic spectral inverse problem.”  ... 

The String Equation and Solitons [chapter]

S. P. Novikov
1996 String Gravity and Physics at the Planck Energy Scale  
Several new approaches were developed for the investigation of this equation on the base of technics of the Theory of Solitons (see [33] [34] [35] [36] [37] ).  ...  This observation leads to some analog of the Lax representation for this Painleve'-1 equation.  ...  We are going to present here some brief survey of the results of Theory of Solitons (see [1] [2] [3] ) from the viewpoint of periodic theory including some new results in the theory of 2-dimensional periodic  ... 
doi:10.1007/978-94-009-0237-4_1 fatcat:aviarmuosncirjhov6a6xyqyem

Page 20 of Mathematical Reviews Vol. , Issue 90H [page]

1990 Mathematical Reviews  
The fundamental group of a topos is normally described as a for- mal inverse system of (discrete) groups; it is well known that if one actually computes the inverse limit of such a system (in the cat-  ...  In that paper it was shown that the cyclic homology could be calculated for singular curves in characteristic zero and, if the KABI conjecture were true, one could also calculate the K-theory of curves  ... 

The String Equation and Solitons [article]

S. P. Novikov
1995 arXiv   pre-print
We present a brief survey of the results of the Theory of Solitons from the viewpoint of the periodic theory including some new results in the theory of 2-dimensional periodic Schrodinger Operators.  ...  Riemann surfaces and Cyclic and semicyclic chains of Laplace transformations (new results of the present author and A.Veselov).  ...  Several new approaches were developed for the investigation of this equation on the base of technics of the Theory of Solitons (see [33] [34] [35] [36] [37] ).  ... 
arXiv:hep-th/9512094v1 fatcat:wibjjofyfzdc5pfevyovvfdwdu

Page 5864 of Mathematical Reviews Vol. , Issue 90J [page]

1990 Mathematical Reviews  
He is able to show that Tor”,(F2, Ry (F2)) = Tor¥,(Fo, F:) and consequently, that an inverse limit of a system gotten by applying the Steinberg idem- potent to terms in an inverse system of quadratic constructions  ...  is 2-cyclic for all k, and cyclic if and only if k = 0, 1, or 3 The author derives some basic properties of n-cyclic maps and uses them on the problem: Which path components of map(SX, Y) have the same  ... 

Page 7286 of Mathematical Reviews Vol. , Issue 94m [page]

1994 Mathematical Reviews  
This cyclic cohomology is important in the study of secondary characteristic classes, as was shown by P. Baum and A. Connes [“K-theory for actions of discrete groups”, Preprint, 1986; per bibl.].”  ...  This book has a very clear introduction (Chapter I) that contains the main results proved in the following chapters and some examples useful for understanding the meaning of the constructions.  ... 

Bivariant twisted cyclic theory and spectral sequences of crossed products

Donggeng Gong
1992 Journal of Pure and Applied Algebra  
As a consequence, we obtain the spectral sequences of bivariant cyclic theory of crossed products and the six-term exact sequences of periodic bivariant cyclic theory for certain groups acting on trees  ...  In Section 4 we USC the bivariant twisted cyclic theory to obtain the spectral sequences of bivariant cyclic theory of crossed products. which generalize that of Brylinski (21 and Feigin and Tsygan [ll  ...  Therefore, we obtain the first six-term exact sequence (26)  ... 
doi:10.1016/0022-4049(92)90052-h fatcat:dmitryzy7jfuvjxsxxvezx2d4q

Page 435 of Mathematical Reviews Vol. 13, Issue 5 [page]

1952 Mathematical Reviews  
Spectral theory and harmonic analysis. Proceedings of the Symposium on Spectral Theory and Differential Problems, pp. 209-219.  ...  In a first section on inverse spectra it is proved that if all the groups of the spectrum are involutory then the limit group is also involutory.  ... 

Page 3404 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
This trellis and its construction algorithm are given for the class of cyclic-form codes. Using the cyclic-form structure of @@R(r,m,/), the 2'-section SRTD of this code is determined.  ...  The best codes or the best known codes for these two classes of convolutional codes are found by computer search. Some of them are better than those found in the past.  ... 

Page 1111 of Mathematical Reviews Vol. 21, Issue 10 [page]

1960 Mathematical Reviews  
In the dual theory, homology groups are replaced by cohomology groups and self-linking in the torsion subgroups of the former by a dual product operation —, in the torsion sub-groups of the latter.  ...  This paper develops a cohomological dual of the theory of self-linking in the homology groups of an oriented manifold.  ... 

Continued Fractions, Wavelet Time Operators and Inverse Problems

Karl Gustafson
2003 Rocky Mountain Journal of Mathematics  
In that conversation I asked, "what is the spectral theory (of the first three topics)?" and a few days later I found the recent paper [27] in my mailbox.  ...  The spectral properties of the analytic theory of continued fractions, orthogonal functions, and rational approximation, are examined from the point of view of operator theory.  ...  I would like to thank Olaf Njåstad for his interest and useful suggestions for the improvement of the preliminary draft of this paper which I circulated at the conference. Also Professor  ... 
doi:10.1216/rmjm/1181069972 fatcat:radoh3ef3fcyhb6l3erut2v2ka

Page 1964 of Mathematical Reviews Vol. 51, Issue 6 [page]

1976 Mathematical Reviews  
., and Lemma 2 states that h lifts to a locally cyclic H whenever some odd multiple of the branch curve of index two in M is homologous to zero.  ...  Using the spectral sequence given by M. Atiyah for equivariant K-theory, the author determines the groups indicated in the title.  ... 
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