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Some Constructions in the Inverse Spectral Theory of Cyclic Groups

2003
*
Combinatorics, probability & computing
*

We show that a recent result

doi:10.1017/s0963548302005436
fatcat:23jq3ifzhrcwrmxrncllzgry7u
*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*. ...##
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Rational algebraic $K$-theory of certain truncated polynomial rings

1985
*
Proceedings of the American Mathematical Society
*

Our method is homological calculation which is facilitated by

doi:10.1090/s0002-9939-1985-0801322-4
fatcat:kaihmk6qarbpvagdigiqlsfibq
*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"( ...##
###
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.” ...

##
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The String Equation and Solitons
[chapter]

1996
*
String Gravity and Physics at the Planck Energy Scale
*

Several new approaches were developed for

doi:10.1007/978-94-009-0237-4_1
fatcat:aviarmuosncirjhov6a6xyqyem
*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 ...##
###
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]

1995
*
arXiv
*
pre-print

We present a brief survey

arXiv:hep-th/9512094v1
fatcat:wibjjofyfzdc5pfevyovvfdwdu
*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] ). ...##
###
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

1992
*
Journal of Pure and Applied Algebra
*

As a consequence, we obtain

doi:10.1016/0022-4049(92)90052-h
fatcat:dmitryzy7jfuvjxsxxvezx2d4q
*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) ...##
###
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

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 ...

##
###
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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