the graded witt group kernel of biquadratic extensions in characteristic two baeza showed that when char f 2 if e f is the separable biquadratic extension e f 1 b1 1 b2 then ker wq f wq e wf 1 b1 wf 1 b2 here we give the analogous result for the graded witt group specifically we obtain an exact sequence f n 1 f n 1 h2n 1f h2n 1e from which the result for gwqf follows by the isomorphisms of kato applications to 2 algebras of exponent and index 4 are also given

invariant subspaces dilation theory and the structure of the predual of a dual algebra i on etudie la structure des preduaux d algebres d operateurs on obtient un nouveau theoreme de sous espace invariant on trouve des proprietes concernant le treillis sous espace invariant de l operateur decalage de bergman

approximation in the mean by polynomials for a positive measure al with compact support in the complex plane c and for 1 t co let pt i denote the closure in lt i of the polynomials in one complex variable the purpose of this paper is to describe pt a the main results are the following first there exists a borel partition ail of the support of al such that for i 1 the space pt t laai contains no nontrivial characteristic functions and

cohomology and graded witt group kernels for extensions of degree four in characteristic two abstract in earlier work the authors determined the graded witt kernel g w q e f ker g w q f g w q e when e f is a biquadratic extension in characteristic 2 by calculating the cohomological kernel h 2 e f ker h 2 f h 2 e in this paper this result is extended to the cases where e f 4 and e is either cyclic or has dihedral galois closure in addition the use of izhboldin s q groups is generalized to obtain six term exact sequences that describe the behavior of these graded rings whenever four term exact sequences and homotopies describe the arithmetic of the extension these tools are valid in characteristic p although the applications here are in characteristic 2

new optimal ternary linear codes the class of quasi twisted qt codes is a generalization of the class of quasi cyclic codes similar to the way constacyclic codes are a generalization of cyclic codes in this paper rate 1 p qt codes over gf 3 are presented which have been constructed using integer linear programming and heuristic combinatorial optimization many of these attain the maximum possible minimum distance for any linear code with the given parameters and several improve the maximum known minimum distances two of these new codes namely 90 6 57 and 120 6 78 are optimal and so prove that d sub 3 90 6 57 and d sub 3 120 6 78

the behavior of differential quadratic and bilinear forms under purely inseparable field extensions abstract let f be a field of characteristic p and let e f be a purely inseparable field extension we study the group h p n 1 f coker f n f n d f n 1 of classes of differential forms under the extension e f and give a system of generators of h p n 1 e f in the case p 2 we use this to determine the kernel w q e f of the restriction map w q f w q e between the groups of nonsingular quadratic forms over f and over e we also deduce the corresponding result for the bilinear witt kernel w e f of the restriction map w f w e where e f denotes a modular purely inseparable field extension

some sufficient conditions for the division property of invariant subspaces in weighted bergman spaces the authors consider weighted bergman spaces of holomorphic l sp p integrable functions with respect to certain borel measures on a bounded plane region a closed subspace scr m of such a space is said to be invariant if z scr m subset scr m in the case of the standard bergman space of the unit disk with p 2 the authors proved in a recent joint paper with c sundberg acta math 177 1996 no 2 275 310 mr1440934 98a 46034 that every invariant subspace scr m is generated by a wandering subspace scr m ominus z scr m for the shift operator thus obtaining an analogue of the celebrated theorem of beurling an invariant space is said to have the division property if the quotient space scr m z lambda scr m is one dimensional for any lambda in the domain under certain additional hypotheses this is equivalent to the codimension one property studied earlier by s richter h hedenmalm k seip and others the main results of this paper are various sufficient conditions for an invariant subspace to have the division property in terms of the local boundary behavior of the functions in the subspace a function f analytic in the unit disc is said to be locally nevanlinna near a point lambda on the unit circle if the subharmonic function log f has a harmonic majorant in the carleson type set obtained by intersecting the unit disk with some disc centered at lambda the authors show that an invariant subspace scr m of the standard bergman space a sp p sb alpha with radial weights 1 z sp 2 sp alpha p ge 1 alpha 1 possesses the division property if some nonzero function f in the subspace is locally nevanlinna at a boundary point they observe that given an invariant subspace scr m which does not have the division property it will always contain two functions such that the space they generate does not have it either it is therefore a question of interest to determine under what conditions the space generated by two functions will possess this property the authors prove the following theorem let 1 le p infty 1 r 1 s 1 p and let f and g be two nonzero functions in a sp p such that f is locally r integrable and g is locally s integrable both in a neighborhood of a boundary point of the disc then the closed linear span of the cyclic invariant subspaces generated by f and by g has the division property an example is also given based on the earlier results of hedenmalm and seip which shows that the theorem is in a way sharp for p 2 the main results also have some interesting corollaries listed in the paper less

the witt group of a discretely valued field abstract this note provides an extension of a classical result of springer in the algebraic theory of quadratic forms for discretely valued fields to the dyadic case

graded witt kernels of the compositum of multiquadratic extensions with the function fields of pfister forms abstract let f be a field of characteristic 2 and w q f be the witt group of nonsingular quadratic forms over f let be a bilinear pfister form over f and l be a multiquadratic extension of f of separability degree less than of equal to 2 in this paper we compute the kernel of the natural homomorphism h 2 m 1 f h 2 m 1 l where h 2 m 1 f is the cokernel of the artin schreier operator f m f m d f m 1 given by x d x 1 x 1 d x m x m x 2 x d x 1 x 1 d x m x m where f m is the space of m differential forms over f and f is the function field of the affine quadric given by the diagonal quadratic form associated to the bilinear form as a consequence we deduce the kernel of the natural homomorphisms i q m 1 f i q m 1 l and i q m 1 f i q m 1 l where i q m 1 f denotes the quotient i q m 1 f i q m 2 f such that i q m 1 f i m f w q f and i m f is the m th power of the fundamental ideal if of the witt ring of f bilinear forms we also include some results concerning the case where is replaced by a bilinear pfister neighbor or a quadratic pfister form

on some invariants of fields of characteristic p 0 abstract let k be a field of characteristic p 0 k n the k vector space of n differential forms and k n k n d k n 1 the artin schreier operator given by x d x 1 x 1 d x n x n x p x d x 1 x 1 d x n x n let h p n 1 k coker and define p k min m h p m 1 k 0 we show that for any finite extension l k p k p l p k 1

wild pfister forms over henselian fields k theory and conic division algebras the epicenter of this paper concerns pfister quadratic forms over a field f with a henselian discrete valuation all characteristics are considered but we focus on the most complicated case where the residue field has characteristic 2 but f does not we also prove results about round quadratic forms composition algebras generalizations of composition algebras we call conic algebras and central simple associative symbol algebras finally we give relationships between these objects and kato s filtration on the milnor k groups of f

symmetric bilinear forms quadratic forms and milnor k theory in characteristic two is bijective for any field f of characteristic two and for any n 0 here k f is the k group of milnor defined in 11 and i is the unique maximal ideal of the witt ring w f of non degenerate symmetric bilinear forms over f on the other hand sah studied quadratic forms in characteristic two in 15 let f be a field of characteristic two wq f the witt group of non degenerate quadratic forms over f and define i wq f n o by the canonical w f module structure on wq f then he proved that wq f iwq f is isomorphic to the group of quadratic cyclic extensions of f and iwq f i2wq f is isomorphic to the subgroup br f 2 of the brauer group br f of f consisting of elements annihilated by 2 in this paper we prove the above milnor s conjecture and describe the precise structures of w f and wq f generalizing the result of sah for any field f of characteristic p 0 let be the n th exterior power over f of the absolute differential module n t g21 let d 2 1 be the f z f fp image of the exterior derivation d f2 t f2 and let v n v resp h 1 f be the kernel resp cokernel of the homomorphism

a generalization of the cellular indecomposable property via fiber dimension abstract the cellular indecomposable property introduced by olin and thomson in 1984 11 is well known for the dirichlet space but it fails trivially for the vector valued case the purpose of this paper is to use the fiber dimension to reformulate the property such that it naturally extends the scalar valued case yet fix the vector valued case in a meaningful way using the new formulation we are able to generalize several previous results to the vector valued setting in particular we extend a theorem of bourdon relating the cellular indecomposable property and the codimension one property to codimension n several of our results appear to be new even for the hardy space over the unit disc

the behavior of quadratic and differential forms under function field extensions in characteristic two abstract let f be a field of characteristic 2 let n f be the f space of absolute differential forms over f there is a homomorphism n f n f d n 1 f given by x d x 1 x 1 d x n x n x 2 x d x 1 x 1 d x n x n mod d f n 1 let h n 1 f coker we study the behavior of hn 1 f under the function field f f where b1 bn is an n fold pfister form and f is the function field of the quadric 0 over f we show that ker h n 1 f h n 1 f f d b 1 b 1 d b n b n using kato s isomorphism of hn 1 f with the quotient inwq f in 1wq f where wq f is the witt group of quadratic forms over f and i w f is the maximal ideal of even dimensional bilinear forms over f we deduce from the above result the analogue in characteristic 2 of knebusch s degree conjecture i e inwq f is the set of all classes q with deg q n

an invariant subspace of the bergman space having the codimension two property nutzungsbedingungen digizeitschriften e v gewahrt ein nicht exklusives nicht ubertragbares personliches und beschranktes recht auf nutzung dieses dokuments dieses dokument ist ausschlieslich fur den personlichen nicht kommerziellen gebrauch bestimmt das copyright bleibt bei den herausgebern oder sonstigen rechteinhabern als nutzer sind sie sind nicht dazu berechtigt eine lizenz zu ubertragen zu transferieren oder an dritte weiter zu geben die nutzung stellt keine ubertragung des eigentumsrechts an diesem dokument dar und gilt vorbehaltlich der folgenden einschrankungen sie mussen auf samtlichen kopien dieses dokuments alle urheberrechtshinweise und sonstigen hinweise auf gesetzlichen schutz beibehalten und sie durfen dieses dokument nicht in irgend einer weise abandern noch durfen sie dieses dokument fur offentliche oder kommerzielle zwecke vervielfaltigen offentlich ausstellen auffuhren vertreiben oder anderweitig nutzen es sei denn es liegt ihnen eine schriftliche genehmigung von digizeitschriften e v und vom herausgeber oder sonstigen rechteinhaber vor mit dem gebrauch von digizeitschriften e v und der verwendung dieses dokuments erkennen sie die nutzungsbedingungen an

some ternary and quaternary codes and associated sphere packings tables of good ternary and quaternary codes are presented and they are used in the construction of dense sphere packings results include 1 tables of the best ternary and quaternary constacyclic codes including cyclic codes up to block length 50 2 a class of optimal n 2 codes over gf q 3 the u v w mod 2u v mod u construction a new ternary code construction technique that can be used to construct the ternary reed muller codes and others and 4 tables of linear ternary and quaternary codes obtained by modifying and combining various codes here and in the literature packings are generated in even dimensions up to 100 using these codes and a sphere packing construction in dimensions 36 and 60 new record densities appear to have been achieved

relations in in and inwq in characteristic 2 abstract let k be a field of characteristic 2 we give natural presentations of the subgroups i n k of the witt ring w k of k and the subgroups i n w q k of the witt group w q k of k our results generalize the results of arason and elman in j k arason r elman powers of the fundamental ideal in the witt ring j algebra 239 2001 150 160 where the characteristic is assumed to be different from 2

nontangential limits in pt µ spaces and the index of invariant subgroups let mu be a finite positive measure on the closed disk d over bar in the complex plane let 1 t infinity and let p t mu denote the closure of the analytic polynomials in l t mu we suppose that d is the set of analytic bounded point evaluations for p t mu and that p t mu contains no nontrivial characteristic functions it is then known that the restriction of mu to partial derivative d must be of the form h vertical bar dz vertical bar we prove that every function f is an element of p t mu has nontangential limits at h vertical bar dz vertical bar almost every point of partial derivative d and the resulting boundary function agrees with f as an element of l t h vertical bar dz vertical bar our proof combines methods from james e thomson s proof of the existence of bounded point evaluations for p t mu whenever p t mu not equal l t mu with xavier tolsa s remarkable recent results on analytic capacity these methods allow us to refine thomson s results somewhat in fact for a general compactly supported measure nu in the complex plane we are able to describe locations of bounded point evaluations for p t nu in terms of the cauchy transform of an annihilating measure as a consequence of our result we answer in the affirmative a conjecture of conway and yang we show that for 1 t infinity dim m zm 1 for every nonzero invariant subspace m of p t mu if and only if h not equal 0 we also investigate the boundary behaviour of the functions in p t mu near the points z is an element of partial derivative d where h z 0 in particular for 1 t infinity we show that there are interpolating sequences for p t mu that accumulate nontangentially almost everywhere on z h z 0 less

linear graph transformations on spaces of analytic functions let h be a hilbert space of analytic functions with multiplier algebra m h and let m f t 1 f t n 1 f f is an element of d be an invariant graph subspace for m h n here n 2 d subset of h is a vector subspace t i d h are linear transformations that commute with each multiplication operator m phi is an element of m h and m is closed in h n in this paper we investigate the existence of non trivial common invariant subspaces of operator algebras of the type a m a is an element of b h ad subset of d at i f t i af for all f is an element of d in particular for the bergman space l 0 2 we exhibit examples of invariant graph subspaces of fiber dimension 2 such that a m does not have any nontrivial invariant subspaces that are defined by linear relations of the graph transformations for m c 2015 elsevier inc all rights reserved less

differential forms and bilinear forms under field extensions abstract let f be a field of characteristic p 0 let n f be the f vector space of n differentials of f over f p let k f g be the function field of an irreducible polynomial g in m 1 variables over f we derive an explicit description of the kernel of the restriction map n f n k as an application in the case p 2 we determine the kernel of the restriction map when passing from the witt ring resp graded witt ring of symmetric bilinear forms over f to that over such a function field extension k

bounded point evaluations for rationally multicyclic subnormal operators abstract let s be a pure bounded rationally multicyclic subnormal operator on a separable complex hilbert space h and let m z be the minimal normal extension on a separable complex hilbert space k containing h let b p e s be the set of bounded point evaluations and let a b p e s be the set of analytic bounded point evaluations we show a b p e s b p e s i n t s the result affirmatively answers a question asked by j b conway concerning the equality of the interior of b p e s and a b p e s for a rationally multicyclic subnormal operator s as a result if 0 i n t s and d i m k e r s 0 n where n is the minimal number of cyclic vectors for s then the range of s 0 is closed hence 0 s e s

new optimal binary linear codes of dimensions 9 and 10 eighteen new codes are presented which improve the bounds on maximum minimum distance for binary linear codes they are rate m r pm r spl ges 1 degenerate quasi cyclic qc codes based on the known upper bounds six of these new codes are optimal in addition five two weight qc codes of dimension 8 are given

annihilators of quadratic and bilinear forms over fields of characteristic two abstract let f be a field with 2 0 w f the witt ring of symmetric bilinear forms over f and w q f the w f module of quadratic forms over f let i f w f be the maximal ideal we compute explicitly in i f m and i m w q f the annihilators of n fold bilinear and quadratic pfister forms thereby answering positively in the case 2 0 certain conjectures stated by kruskemper in m kruskemper on annihilators in graded witt rings and in milnor s k theory in b jacob et al eds recent advances in real algebraic geometry and quadratic forms in contemp math vol 155 1994 pp 307 320

some new results for ternary linear codes of dimension 5 and 6 it is proved that ternary codes with parameters 40 5 25 and 148 5 98 do not exist a new ternary code is constructed with parameters 47 5 30 the results solve the problem of finding the smallest n for which a ternary n 5 d code exists for d 25 29 30 and 98 several new ternary linear codes of dimension 6 are found including one two weight code giving rise to a new strongly regular graph

cohomological kernels of mixed extensions in characteristic 2 abstract let f be a field of characteristic 2 f m the space of m differential forms over f d f m 1 f m the differential operator and h 2 m 1 f the cokernel of the artin schreier operator f m f m d f m 1 given on generators by x d x 1 x 1 d x m x m x 2 x d x 1 x 1 d x m x m d f m 1 it was shown in 8 that given a multiquadratic purely inseparable extension l f and a separable quadratic extension k f then the kernel of the natural homomorphism h 2 m 1 f h 2 m 1 k l is equal to the sum of the kernels of the extensions l f and k f in this paper we extend this result to the compositum of a finite purely inseparable multiquadratic extension with a separable biquadratic extension and we prove that this splitting property of kernels is no longer true by computing the kernel of the compositum of a separable quadratic or biquadratic extension with a simple purely inseparable extension of arbitrary degree

some best rate 1 p and rate p 1 p systematic quasi cyclic codes over gf 3 and gf 4 the class of quasi cyclic qc codes has been proven to contain many good codes to date the known qc codes are primarily rate 1 p and p 1 p binary codes constructed from circulant matrices these results are extended to qc codes over gf 3 and gf 4 codes are constructed using integer linear programming and heuristic combinatorial optimization many of these attain the maximum possible minimum distance for any linear code with the same parameters and several improve the maximum known distances the link between power residue pr codes and qc codes is exploited as a means of constructing new qc codes and to initialize the search algorithm previously unknown minimum distances for nonbinary quadratic residue codes are given the minimum distances for the pr codes and the maximum known distances for the qc codes are tabulated

new optimal quaternary linear codes of dimension 5 in this correspondence new optimal quaternary linear codes of dimension 5 are presented which extend previously known results these codes belong to the class of quasi twisted qt codes and have been obtained using a greedy local search algorithm other codes are also given which provide a lower bound on the maximum possible minimum distance the generator polynomials for these codes are tabulated and the minimum distances of known qt codes are given