on convex vector precoding for multiuser mimo broadcast channels we propose different convex alphabet relaxation schemes for vector precoding in mimo broadcast channels using binary quaternary and octonary modulation expressions are presented for the probability of the different precoding schemes to achieve interference free communication over singular channels the energy of transmission is evaluated in the many user limit using the replica method from statistical physics an alternative channel inversion technique is proposed which makes purely real binary alphabets perform as well as their complex extensions resulting in reduced complexity in the optimization process the relevance of the asymptotic analysis is confirmed by finite size simulations

identification of simple representations for affine q schur algebras abstract we define an explicit action of the quantum loop algebra u q gl n on the tensor space and show that these actions are compatible with the natural embedding u q gl n u q gl n 1 as an application we identify simple representations of affine q schur algebras s n r c arising from simple polynomial representations of u q gl n frenkel and mukhin 2002 11 with those arising from simple modules of the affine hecke algebra h r c of type a rogawski 1985 26

difference of weighted composition operators abstract we obtain complete characterizations in terms of carleson measures for bounded compact differences of weighted composition operators acting on the standard weighted bergman spaces over the unit disk unlike the known results we allow the weight functions to be non holomorphic and unbounded as a consequence we obtain a compactness characterization for differences of unweighted composition operators acting on the hardy spaces in terms of carleson measures and as a nontrivial application of this we show that compact differences of composition operators with univalent symbols on the hardy spaces are exactly the same as those on the weighted bergman spaces as another application we show that an earlier characterization due to acharyya and wu for compact differences of weighted composition operators with bounded holomorphic weights does not extend to the case of non holomorphic weights we also include some explicit examples related to our results

essential norms of weighted composition operators and aleksandrov measures abstract we derive exact formulas for the essential and weak essential norms of weighted analytic composition operators acting on certain function spaces in the unit disc extending and improving earlier results due to sarason and to kriete and moorhouse differences of composition operators are also considered the formulas involve the aleksandrov measures associated to the symbol of the operator the results are based on a variant of a general method due to weis of constructing best compact and weakly compact approximants for linear operators on l 1 spaces

hilbert schmidt differences of composition operators on the bergman space in the setting of the weighted bergman space over the unit disk we characterize hilbert schmidt differences of two composition operators in terms of integrability condition involving pseudohyperbolic distance between the inducing functions we also show that a linear combination of two composition operators can be hilbert schmidt except for trivial cases only when it is essentially a difference we apply our results to study the topological structure of the space of all composition operators under the hilbert schmidt norm topology we first characterize components and then provide some sufficient conditions for isolation or for non isolation

on compactness of the difference of composition operators abstract let and be analytic self maps of the unit disc and denote by c and c the induced composition operators the compactness and weak compactness of the difference t c c are studied on h p spaces of the unit disc and l p spaces of the unit circle it is shown that the compactness of t on h p is independent of p 1 the compactness of t on l 1 and m the space of complex measures is characterized and examples of and are constructed such that t is compact on h 1 but non compact on l 1 other given results deal with l weakly compact counterparts of the previous results and a conjecture of j e shapiro

an application of atomic decomposition in bergman spaces to the study of differences of composition operators abstract in this paper we characterize bounded differences of composition operators from standard weighted bergman spaces a p into lebesgue spaces l q when 1 and p q in the process we also find an interesting connection between the difference operator and certain weighted composition operators answering a question raised in saukko 2011 18 by combining the results of this paper with those of saukko 2011 18 we obtain a complete characterization of bounded and compact differences between standard weighted bergman spaces

spectral theory for algebraic combinations of toeplitz and composition operators abstract we determine the essential spectra of algebraic combinations of toeplitz operators with continuous symbol and composition operators induced by a class of linear fractional non automorphisms of the unit disk the operators in question act on the hardy space h 2 on the unit disk our method is to realize the c algebra that they generate as an extension of the compact operators by a concrete c algebra whose invertible elements are easily characterized

q tensor space and q weyl modules we obtain the irreducible representations of the q schur algebra motivated by the fact that these representations give all the irreducible representations of gln q in the nondescribing characteristic the irreducible polynomial representations of the general linear groups in the describing characteristic are a special case of this construction the theory of polynomial representations of general linear groups is equivalent to the representation theory of schur algebras see green s book 5 and the bibliography therein in 4 we defined q analogues of schur algebras when q 1 these are the usual schur algebras and when q is a prime power representations of q schur algebras give a substantial part of the representation theory of finite general linear groups in the nondescribing characteristic case including all irreducible representations of these groups and important information about decomposition numbers it is natural to ask what features of the classical schur algebras have qanalogues in this paper we define q analogues of tensor space of weyl modules and of weight spaces thereby generalizing the main reslllts which appear in green s book 5 for example we classify the irreducible modules for qschur algebras we determine bases for q weyl modules compatible with weight spaces and we give results on composition multiplicities of the irreducible modules in q weyl modules the proofs are largely self contained so by specializing q to 1 we recover the corresponding results in 5 this paper therefore is relevant to the representation theory of symmetric groups and to the representation theory of general linear groups in the describing and in the nondescribing characteristics 1 the q schur algebra let r be a natural number let r be an integral domain and let q be a unit in r we denote the symmetric group on r letters by er the hecke algebra z is the r free r algebra with basis twlw e er where the multiplication is determined by the following rule if a i i 1 is a basic transposition in received by the editors august 15 1989 1980 mathematics subject classification 198 5 revision primary 1 6a64 1 6a6 5 secondary 20c30 this research was supported in part by nsf grant no dms 8802290 the authors gratefully acknowledge support received from nato grant no 0222 87 r 1991 american mathematical society 0002 9947 91 1 00 25 per page

difference of composition operators between different hardy spaces abstract some estimates for the norm and essential norm of the difference of two composition operators between different hardy spaces are given in this paper

compact linear combination of composition operators on bergman spaces abstract motivated by the question of shapiro and sundberg raised in 1990 study on linear combinations of composition operators has been a topic of growing interest in this paper we completely characterize the compactness of any finite linear combination of composition operators with general symbols on the weighted bergman spaces in two classical terms one is a function theoretic characterization of julia caratheodory type and the other is a measure theoretic characterization of carleson type our approach is completely different from what has been known so far

compact linear combinations of composition operators induced by linear fractional maps it has been known that the difference of two composition operators induced by linear fractional self maps of a ball cannot be nontrivially compact on either the hardy space or any standard weighted bergman space in this paper we extend this result in two significant directions the difference is extended to general linear combinations and inducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension

boundary correspondence of nevanlinna counting functions for self maps of the unit disc let be a holomorphic self map of the unit disc d for every a d there is a measure on d sometimes called aleksandrov measure defined by the poisson representation re z z f p z d its singular part measures in a natural way the affinity of for the boundary value a the affinity for values w inside d is provided by the nevanlinna counting function n w of we introduce a natural measure valued refinement m w of n w and establish that the measures d are obtained as boundary values of the refined nevanlinna counting function m more precisely we prove that is the weak limit of m w whenever w converges to a non tangentially outside a small exceptional set e we obtain a sharp estimate for the size of e in the sense of capacity

linear relations in the calkin algebra for composition operators we consider this and related questions when is a finite linear combination of composition operators acting on the hardy space or the standard weighted bergman spaces on the unit disk a compact operator

presenting q schur algebras as quotients of the quantized enveloping algebra of sln in the work of doty and giaquinto int math res not 36 1907 2002 and du and parshall trans am math soc 355 1593 2003 the presentations of q schur algebra as a quotient of quantum gln are given doty and giaquinto electron res announce am math soc 7 54 2001 obtained the presentation for the schur algebra u 2 r and q schur algebra u 2 r as a quotient of classical quantized enveloping algebra of sl2 respectively they pointed out that the problem of presenting q schur algebra u n r as a quotient of quantized enveloping algebra of sln seems to be more difficult for n 2 inspired by this point of view we obtain a presentation for the schur algebra both the classical and quantized case as a quotient of classical quantized enveloping algebra of sln respectively in this paper in the work of doty and giaquinto int math res not 36 1907 2002 and du and parshall trans am math soc 355 1593 2003 the presentations of q schur algebra as a quotient of quantum gln are given doty and giaquinto electron res announce am math soc 7 54 2001 obtained the presentation for the schur algebra u 2 r and q schur algebra u 2 r as a quotient of classical quantized enveloping algebra of sl2 respectively they pointed out that the problem of presenting q schur algebra u n r as a quotient of quantized enveloping algebra of sln seems to be more difficult for n 2 inspired by this point of view we obtain a presentation for the schur algebra both the classical and quantized case as a quotient of classical quantized enveloping algebra of sln respectively in this paper

joint carleson measure and the difference of composition operators on aαp bn we introduce a concept of joint carleson measure and characterize when the difference of two composition operators on a p bn the weighted bergman space over the unit ball bn in cn is bounded or compact we apply this joint carleson measure characterization to composition operators with smooth symbols and construct an interesting example which shows that the boundedness or the compactness depends on p when n 2 this is in sharp contrast with the single composition operator case where the boundedness or the compactness is independent of p 0 moreover the compact difference on the weighted bergman spaces over the unit disc is known to be independent of p 0 and the compact difference on a p bn is known to be independent of p 0 if each composition operator is bounded on a p bn for some 1 2

difference of composition operators between standard weighted bergman spaces we obtain estimates for the norm and essential norm of the difference of two composition operators between certain bergman spaces in particular a necessary and sufficient condition for boundedness and compactness of the operator is established finally we give a sufficient condition for boundedness and compactness of the difference operator between hardy spaces

presenting affine q schur algebras we obtain a presentation of certain affine q schur algebras in terms of generators and relations the presentation is obtained by adding more relations to the usual presentation of the quantized enveloping algebra of type affine our results extend and rely on the corresponding result for the q schur algebra of the symmetric group which were proved by the first author and giaquinto

on the connected component of compact composition operators on the hardy space we show that there exist non compact composition operators in the connected component of the compact ones on the classical hardy space h2 this answers a question posed by shapiro and sundberg in 1990 we also establish an improved version of a theorem of maccluer giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols as a main tool we use aleksandrov clark measures

compact double differences of composition operators on the bergman spaces abstract as is well known on the weighted bergman spaces over the unit disk compactness of differences of two composition operators is characterized by certain cancellation property of the inducing maps at every bad boundary point which makes each composition operator in the difference fail to be compact recently the second and third authors obtained a result implying that double difference cancellation is not possible for linear combinations of three composition operators in this paper we obtain a complete characterization for compact double differences formed by four composition operators applying our characterization we easily recover known results on linear combinations of two or three composition operators as another application we also show that double difference cancellation is possible for linear combinations of four composition operators by constructing an explicit example of a compact double difference formed by two noncompact differences in spite of such an example our characterization also shows that double difference cancellation may occur in the global sense only and that genuine double difference cancellation is not possible in a certain local sense

linear sums of two composition operators on the fock space abstract linear sums of two composition operators of the multi dimensional fock space are studied we show that such an operator is bounded only when both composition operators in the sum are bounded so cancelation phenomenon is not possible on the fock space in contrast to what have been known on other well known function spaces over the unit disk we also show the analogues for compactness and for membership in the schatten classes for linear sums of more than two composition operators the investigation is left open

q schur algebras as quotients of quantized enveloping algebras abstract we study the properties of the surjective homomorphism defined by beilinson lusztig and macpherson from the quantized enveloping algebra of gl n to the q schur algebra s q n r in particular we find an expression for the preimage of an arbitrary element of s q n r under this map and a basis for the kernel

cancellation properties of composition operators on bergman spaces abstract the compact difference of two composition operators on the bergman spaces over the unit disc is characterized in 11 in terms of certain cancellation property of the inducing maps at every bad boundary points which make each single composition operator not to be compact in this paper we completely characterize the compactness of a linear combination of three composition operators on the bergman space as one consequence of this characterization we show that there is no cancellation property for the compactness of double difference of composition operators more precisely we show that if i are distinct and none of c i is compact then c 1 c 2 c 3 c 1 is compact if and only if both c 1 c 2 and c 3 c 1 are compact

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

components of linear fractional composition operators abstract we determine when two linear fractional composition operators on the hardy space h 2 belong to the same component in the collection of all composition operators on h 2 we show that two such composition operators in the same component may fail to have compact difference which answers a question raised by joel shapiro and carl sundberg

the affineq schur algebra abstract we introduce an analogue of the q schur algebra associated to coxeter systems of type a n 1 we give two constructions of this algebra the first construction realizes the algebra as a certain endomorphism algebra arising from an affine hecke algebra of type a r 1 where n r this generalizes the original q schur algebra as defined by dipper and james and the new algebra contains the ordinary q schur algebra and the affine hecke algebra as subalgebras using this approach we can prove a double centralizer property the second construction realizes the affine q schur algebra as the faithful quotient of the action of a quantum group on the tensor power of a certain module analogous to the construction of the ordinary q schur algebra as a quotient of u g l n