isometric dilations for infinite sequences of noncommuting operators this paper develops a dilation theory for t n l an infinite sequence of noncommuting operators on a hilbert space when the matrix t1 t2 is a contraction a wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for tn i are obtained some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given this results are used to extend the sz nagy foia lifting theorem to this noncommutative setting this paper is a continuation of 5 and develops a dilation theory for an infinite sequence tn n of noncommuting operators on a hilbert space when en 1 tn tn i i is the identity on s many of the results and techniques in dilation theory for one operator 8 and also for two operators 3 4 are extended to this setting first we extend wold decomposition 8 4 to the case of an infinite sequence vn i of isometries with orthogonal final spaces in 2 we obtain a minimal isometric dilation for tn 1 by extending the schaffer construction in 6 4 using these results we give some theorems on the geometric structure of the space of the minimal isometric dilation finally we give some sufficient conditions on a sequence t7 n to be simultaneously quasi similar to a sequence rn n i of isometries on a hilbert space x with en rnrn n ix in 3 we use the above mentioned theorems to obtain the sz nagy foia5 lifting theorem 7 8 1 4 in our setting in a subsequent paper we will use the results of this paper for studying the characteristic function associated to a sequence tn lo 1 with ez 1 t t i throughout this paper a stands for the set 1 2 k k e n or the set n 1 2 received by the editors september 1 1987 1980 mathematics subject classification 1985 revision primary 47a20 secondary 47a45

tensor algebras overc correspondences representations dilations andc envelopes tensor algebras overc correspondences are noncommutative generalizations of the disk algebra they contain as special cases analytic crossed products semi crossed products and popescu s noncommutative disk algebras in this paper a dilation theorem and a commutant lifting theorem for representations of tensor algebras is proved these are used to show that for certainc correspondences thec envelopes in the sense of arveson of the tensor algebras are the cuntz pimsner algebras of the correspondences

isomorphisms of algebras associated with directed graphs given countable directed graphs g and g we show that the associated tensor algebras open image in new window g and open image in new window g are isomorphic as banach algebras if and only if the graphs g are g are isomorphic for tensor algebras associated with graphs having no sinks or no sources the graph forms an invariant for algebraic isomorphisms we also show that given countable directed graphs g g the free semigroupoid algebras open image in new window and open image in new window are isomorphic as dual algebras if and only if the graphs g are g are isomorphic in particular spatially isomorphic free semigroupoid algebras are unitarily isomorphic for free semigroupoid algebras associated with locally finite directed graphs with no sinks the graph forms an invariant for algebraic isomorphisms as well

composition operators on noncommutative hardy spaces abstract in this paper we initiate the study of composition operators on the noncommutative hardy space h ball 2 which is the hilbert space of all free holomorphic functions of the form f x 1 x n k 0 k a x f n a 2 1 where the convergence is in the operator norm topology for all x 1 x n in the noncommutative operatorial ball b h n 1 and b h is the algebra of all bounded linear operators on a hilbert space h when the symbol is a free holomorphic self map of b h n 1 we show that the composition operator c f f f h ball 2 is bounded on h ball 2 several classical results about composition operators boundedness norm estimates spectral properties compactness similarity have free analogues in our noncommutative multivariable setting the most prominent feature of this paper is the interaction between the noncommutative analytic function theory in the unit ball of b h n the operator algebras generated by the left creation operators on the full fock space with n generators and the classical complex function theory in the unit ball of c n in a more general setting we establish basic properties concerning the composition operators acting on fock spaces associated with noncommutative varieties v p 0 h b h n 1 generated by sets p 0 of noncommutative polynomials in n indeterminates such that p 0 0 p p 0 in particular when p 0 consists of the commutators x i x j x j x i for i j 1 n we show that many of our results have commutative counterparts for composition operators on the symmetric fock space and consequently on spaces of analytic functions in the unit ball of c n

invariant subspaces and hyper reflexivity for free semigroup algebras in this paper we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras this enables us to prove that they are reflexive and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces such algebras are called hyper reflexive this property is very strong but it has been established in only a very few cases moreover the prototypes of this class of algebras are the natural candidate for a non commutative analytic toeplitz algebra on n variables the case we make for this analogy is very compelling in particular in this paper the key to the invariant subspace analysis is a good analogue of the beurling theorem for invariant subspaces of the unilateral shift this leads to a notion of inner outer factorization in these algebras in a sequel to this paper 13 we add to this evidence by showing that there is a natural homomorphism of the automorphism group onto the group of conformal automorphisms of the ball in cn a free semigroup algebra is the weak operator topology closed algebra generated by a set s1 sn of isometries with pairwise orthogonal ranges these conditions are described algebraically by s i sj iji for 1 i j n f

caratheodory interpolation on the non commutative polydisk the caratheodory problem in the n variable non commutative herglotz agler class and the caratheodory fejer problem in the n variable non commutative schur agler class are posed it is shown that the caratheodory resp caratheodory fejer problem has a solution if and only if the non commutative polynomial with given operator coefficients the data of the problem indexed by an admissible set takes operator values with positive semidefinite real part resp contractive operator values on n tuples of jointly nilpotent contractive n n matrices for all n n

the coulomb unitarity relation and some series of products of three legendre functions we obtain from the off shell coulomb unitarity relation a closed expression for j l 0 2l 1 pl x qli y ql i z and we consider some related series of products of legendre functions

e0 dilation of strongly commuting cp0 semigroups abstract we prove that every strongly commuting pair of cp 0 semigroups has a minimal e 0 dilation this is achieved in two major steps interesting in themselves 1 we show that a strongly commuting pair of cp 0 semigroups can be represented via a two parameter product system representation 2 we prove that every fully coisometric product system representation has a fully coisometric isometric dilation in particular we obtain that every commuting pair of cp 0 semigroups on b h h finite dimensional has an e 0 dilation

numerical computations of supersonic base flow with special emphasis on turbulence modeling abstract a zonal implicit time marching navier stokes computational technique has been used to compute the turbulent supersonic base flow over cylindrical afterbodies a critical element of calculating such flows is the turbulence model various eddy viscosity turbulence models have been used in the base region flow computations these models include two algebraic turbulence models and a two equation k epsilon model the k epsilon equations are developed in a general coordinate system and solved using an implicit algorithm calculations with the k epsilon model are extended up to the wall flow field computations have been performed for a cylindrical afterbody at m 2 46 and at angle of attack alpha 0 the results are compared to the experimental data for the same conditions and the same configuration details of the mean flow field as well as the turbulence quantifies have been presented in addition the computed base pressure distribution has been compared with the experiment in general the k epsilon turbulence model performs better in the near wake than the algebraic models and predicts the base pressure much better base flow base pressure turbulence models wake supersonic flow

the algebraic structure of non commutative analytic toeplitz algebras the non commutative analytic toeplitz algebra is the wot closed algebra generated by the left regular representation of the free semigroup on n generators we develop a detailed picture of the algebraic structure of this algebra in particular we show that there is a canonical homomorphism of the automorphism group onto the group of conformal automorphisms of the complex n ball the k dimensional representations form a generalized maximal ideal space with a canonical surjection onto the ball of k kn matrices which is a homeomorphism over the open ball analogous to the fibration of the maximal ideal space of h over the unit disk in 6 17 18 20 a good case is made that the appropriate analogue for the analytic toeplitz algebra in n non commuting variables is the wotclosed algebra generated by the left regular representation of the free semigroup on n generators the papers cited obtain a compelling analogue of beurling s theorem and inner outer factorization in this paper we add further evidence the main result is a short exact sequence determined by a canonical homomorphism of the automorphism group onto this algebra onto the group of conformal automorphisms of the unit ball of cn the kernel is the subgroup of quasi inner automorphisms which are trivial modulo the wot closed commutator ideal additional evidence of analytic properties comes from the structure of k dimensional completely contractive representations which have a structure very similar to the fibration of the maximal ideal space of h over the unit disk an important tool in our analysis is a detailed structure theory for wot closed right ideals curiously left ideals remain more obscure the non commutative analytic toeplitz algebra ln is determined by the left regular representation of the free semigroup fn on n generators z1 zn which acts on 2 fn by w v wv for v w in fn in particular the algebra ln is the unital wot closed algebra generated by the isometries li zi for 1 i n this algebra and its norm closed version the noncommutative disk algebra were introduced by popescu 19 in an abstract sense in connection with a non commutative von neumann inequality and 1991 mathematics subject classification 47d25 march 9 1997 october 9 1997 final draft first author partially supported by an nserc grant and a killam research fellowship second author partially supported by an nsf grant

free holomorphic functions and interpolation in this paper we obtain a noncommutative multivariable analogue of the classical nevanlinna pick interpolation problem for analytic functions with positive real parts on the open unit disc given a function f lambda to mathbb c where lambda is an arbitrary subset of the open unit ball mathbb b n z in mathbb c n z 1 we find necessary and sufficient conditions for the existence of a free holomorphic function g with complex coefficients on the noncommutative open unit ball b mathcal h n 1 such that rm re g geq 0 quad rm and quad g z f z quad z in lambda where b mathcal h is the algebra of all bounded linear operators on a hilbert space mathcal h the proof employs several results from noncommutative multivariable operator theory and a noncommutative cayley transform introduced and studied in the present paper acting from the set of all free holomorphic functions with positive real parts to the set of all bounded free holomorphic functions all the results of this paper are obtained in the more general setting of free holomorphic functions with operator valued coefficients as consequences we deduce some results concerning operator valued analytic interpolation on the unit ball mathbb b n

free pluriharmonic majorants and commutant lifting in this paper we initiate the study of sub pluriharmonic curves and free pluriharmonic majorants on the noncommutative open ball b h n 1 x1 xn b h n x1x1 xnxn 1 2 1 where b h is the algebra of all bounded linear operators on a hilbert space h several classical results from complex analysis have analogues in this noncommutative multivariable setting we present basic properties for sub pluriharmonic curves characterize the class of sub pluriharmonic curves that admit free pluriharmonic majorants and find in this case the least free pluriharmonic majorants we show that for any free holomorphic function on b h n 1 the map 0 1 c r1 rn r rr1 rrn rr1 rrn is a sub pluriharmonic curve in the cuntz toeplitz algebra generated by the right creation operators r1 rn on the full fock space with n generators we prove that is in the noncommutative hardy space hball2 if and only if has a free pluriharmonic majorant in this case we find herglotz riesz and poisson type representations for the least pluriharmonic majorant of moreover we obtain a characterization of the unit ball of hball2 and provide a parametrization and concrete representations for all free pluriharmonic majorants of when is in the unit ball of hball2 in the second part of this paper we introduce a generalized noncommutative commutant lifting gncl problem which extends to our noncommutative multivariable setting several lifting problems including the classical sz nagy foias commutant lifting problem and the extensions obtained by treil volberg foias frazho kaashoek and biswas foias frazho as well as their multivariable noncommutative versions we solve the gncl problem and using the results regarding sub pluriharmonic curves and free pluriharmonic majorants on noncommutative balls we provide a complete description of all solutions in particular we obtain a concrete schur type description of all solutions in the noncommutative commutant lifting theorem

hyperbolic geometry on noncommutative polyballs in this paper we study the noncommutative balls c x1 xn b h n x1 xn 1 0 where is the joint operator radius for n tuples of bounded linear operators on a hilbert space in particular 1 is the operator norm 2 is the joint numerical radius and is the joint spectral radius we introduce a harnack type equivalence relation on c 0 and use it to define a hyperbolic distance on the harnack parts equiv alence classes of c we prove that the open ball c 0 is the harnack part containing 0 and obtain a concrete formula for the hyperbolic distance in terms of the reconstruction operator associated with the right creation operators on the full fock space with n gener ators moreover we show that the topology and the usual operator norm topology coincide on c 1 while the open ball c 1 is not a complete metric space with respect to the operator norm topology we prove that it is a complete metric space with respect to the hyper bolic metric in the particular case when 1 and h c the hyperbolic metric coincides with the poincare bergman distance on the open unit ball of c n

remarks on the interpolation and the similarity problem for nest subalgebras of von neumann algebras abstract given a nest subalgebra of a von neumann algebra a and vectors f g we give necessary and sufficient conditions for the existence of an operator a in a so that af g this generalizes a well known theorem of e c lance and the main result in anoussis 1992 katsoulis et al 1993 we also use the generalized ringrose criterion to show that the similarity problem for continuous nests in certain crossed product factors of type iii has a negative answer

free holomorphic functions on the unit ball of b h n abstract in this paper we continue the study of free holomorphic functions on the noncommutative ball b h n 1 x 1 x n b h n x 1 x 1 x n x n 1 2 1 where b h is the algebra of all bounded linear operators on a hilbert space h and n 1 2 or n several classical results from complex analysis have free analogues in our noncommutative setting we prove a maximum principle a naimark type representation theorem and a vitali convergence theorem for free holomorphic functions with operator valued coefficients we introduce the class of free holomorphic functions with the radial infimum property and study it in connection with factorizations and noncommutative generalizations of some classical inequalities obtained by schwarz and harnack the borel caratheodory theorem is extended to our noncommutative setting using a noncommutative generalization of schwarz s lemma and basic facts concerning the free holomorphic automorphisms of the noncommutative ball b h n 1 we obtain an analogue of julia s lemma for free holomorphic functions f b h n 1 b h m 1 we also obtain pick julia theorems for free holomorphic functions with operator valued coefficients we provide a noncommutative generalization of a classical inequality due to lindelof which turns out to be sharper then the noncommutative von neumann inequality finally we introduce a pseudohyperbolic metric on b h n 1 which is invariant under the action of the free holomorphic automorphism group of b h n 1 and turns out to be a noncommutative extension of the pseudohyperbolic distance on b n the open unit ball of c n in this setting we obtain a schwarz pick type lemma we also provide commutative versions of these results for operator valued multipliers of the drury arveson space

on fixed points of self maps of the free ball abstract in this paper we study the structure of the fixed point sets of noncommutative self maps of the free ball we show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ball with a linear subspace we provide an application for the completely isometric isomorphism problem of multiplier algebras of noncommutative complete pick spaces

a class of sums of gegenbauer functions twenty four sums in closed form series of the type n 0 n c n 1 2 k l m kh 1 c n xh li 1 d n zi m j 1 d n u j are studied here c n is gegenbauer s polynomial also called the ultraspherical polynomial and d n and d n are gegenbauer functions of the second kind interrelationships and analytic properties are discussed and closed forms for 24 of these sums are given more than half of which are new

tensor algebras of c correspondences and their c envelopes abstract we show that the c envelope of the tensor algebra of an arbitrary c correspondence x coincides with the cuntz pimsner algebra o x as defined by katsura t katsura on c algebras associated with c correspondences j funct anal 217 2004 366 401 this improves earlier results of muhly and solel p s muhly b solel tensor algebras over c correspondences representations dilations and c envelopes j funct anal 158 1998 389 457 and fowler muhly and raeburn n fowler p muhly i raeburn representations of cuntz pimsner algebras indiana univ math j 52 2003 569 605 who came to the same conclusion under the additional hypothesis that x is strict and faithful

multivariable nehari problem and interpolation abstract in this paper we obtain a multivariable nehari type theorem for hankel operators extending the classical result as well as treil volberg generalization the result is based on a new generalization of the noncommutative commutant lifting theorem which extends to several variables the commutant lifting result obtained by treil and volberg and recently generalized by biswas foias and frazho an extension of i s iokhvidov ky fan theorem is obtained and used to prove a multivariable adamian arov krein type theorem for generalized hankel operators as consequences we obtain caratheodory and nevanlinna pick type interpolation results for meromorphic operators on fock spaces resp operator valued meromorphic functions on the unit ball of c n the nehari type results are used to obtain descriptions of hankel operators acting on fock spaces or weighted fock spaces multivariable dirichlet type spaces and to solve new weighted interpolation problems e g sarason for noncommutative analytic toeplitz algebras which have consequences to the operator valued analytic interpolation in the unit ball of c n moreover using central intertwining liftings we obtain explicit formulas for certain solutions of the weighted interpolation problems as another application of the generalized noncommutative commutant lifting theorem we derive an abstract interpolation problem for multipliers this is used to solve a left tangential nevanlinna pick type interpolation problem with operatorial argument for noncommutative analytic toeplitz algebras

free biholomorphic functions and operator model theory ii let f f1 fn be an n tuple of formal power series in noncommutative indeterminates z1 zn such that f 0 0 and the jacobian detjf 0 0 and let g g1 gn be its inverse with respect to composition we assume that f and g have nonzero radius of convergence and g is a bounded free holomorphic function on the open unit ball b h n 1 where b h is the algebra of bounded linear operators an a hilbert space h in this paper several results concerning the noncommutative multivariable operator theory on the unit ball b h n 1 are extended to the noncommutative domain bf h x b h n g f x x and f x 1 for an appropriate evaluation x f x we develop an operator model theory and dilation theory for bf h where the associated universal model is an n tuple mz1 mzn of left multiplication operators acting on a hilbert space h2 f of formal power series all the results of this paper have commutative versions

representations of product systems over semigroups and dilations of commuting cp maps we prove that every pair of commuting cp maps on a von neumann algebra m can be dilated to a commuting pair of endomorphisms on a larger von neumann algebra to achieve this we first prove that every completely contractive representation of a product system of c correspondences over the semigroup n2 can be dilated to an isometric or toeplitz representation

multi toeplitz operators and free pluriharmonic functions abstract we initiate the study of weighted multi toeplitz operators associated with noncommutative regular domains d q m h b h n m n 1 where b h is the algebra of all bounded linear operators on a hilbert space h these operators are acting on the full fock space with n generators and have as symbols free pluriharmonic functions on the interior of the domain d q m h we prove that the set of all weighted multi toeplitz operators coincides with a d q m a d q m w o t where the domain algebra a d q m is the norm closed unital non selfadjoint algebra generated by the universal model w 1 w n of the noncommutative domain d q m h these results are used to study the class of free pluriharmonic functions on d q m h several classical results from complex analysis concerning harmonic functions have analogues in our noncommutative setting in particular we show that the bounded free pluriharmonic functions are precisely those which are noncommutative berezin transforms of weighted multi toeplitz operators and solve the dirichlet extension problem in this setting using noncommutative cauchy transforms we provide a free analytic functional calculus for n tuples of operators which extends to free pluriharmonic functions our study of weighted multi toeplitz operators on fock spaces is a blend of multi variable operator theory noncommutative function theory operator spaces and harmonic analysis

dilating covariant representations of the non commutative disc algebras let be an isometric automorphism of the non commutative disc algebra an for n 2 we show that every contractive covariant representation of an dilates to a unitary covariant representation of on hence the c envelope of the semicrossed product an z is on z

hardy algebras w correspondences and interpolation theory given a von neumann algebra m and a w correspondence e over m we construct an algebra h e that we call the hardy algebra of e when m open image in new window e h e is the classical hardy space h open image in new window of bounded analytic functions on the unit disc when m open image in new window and e open image in new window h e is the free semigroup algebra studied by popescu davidson and pitts and many others we show that given any faithful normal representation of m on a hilbert space h there is a natural correspondence e over the commutant m called the dual of e and that h e can be realized in terms of b h valued functions on the open unit ball open image in new window e in the space of adjoints of elements in e we prove analogues of the nevanlinna pick theorem in this setting and discover other aspects of the value distribution theory for elements in h e we also analyze the boundary behavior of elements in h e and obtain generalizations of the sz nagy foias functional calculus and the functional calculus of popescu for c n c row contractions the correspondence e has a dual that is naturally isomorphic to e and the commutants of certain so called induced representations of h e can be viewed as induced representations of h e for these induced representations a double commutant theorem is proved

effective noncommutative nevanlinna pick interpolation in the row ball and applications abstract we provide an effective single matrix criterion in terms of what we call the elementary pick matrix for the solvability of the noncommutative nevanlinna pick interpolation problem in the row ball and provide some applications in particular we show that the so called column row property fails for the free semigroup algebras in stark contrast to the analogous commutative case additional applications of the elementary pick matrix include a local dilation theorem for matrix row contractions and interpolating sequences in the noncommutative setting finally we present some numerical results related to the failure of the column row property

interpolation problems in several variables abstract we obtain a noncommutative nudel man type interpolation theorem in several variables and a commutative analogue forh b n the hardy space of bounded analytic functions in the open ball of c n using this result we obtain an operatorial analogue in several variables of the rosenblum rovnyak restriction theorem as well as an extension to the noncommutative analytic toeplitz algebraf we provide new extensions of the caratheodory fejer and nevanlinna pick interpolation theorems forf

gleason s problem and schur multipliers in the multivariable quaternionic setting abstract we define and study the counterparts of gleason s problem of the drury arveson s space and of schur multipliers when the unit ball of c n is replaced by the unit ball of h n where h denotes the algebra of real quaternions schur multipliers are characterized in terms of coisometric operator matrices in quaternionic spaces finally we define the counterpart of blaschke factors in this setting and study a one point interpolation problem

a family of sums of products of legendre functions we present simple analytic expressions for a few sums of products of legendre functions of the type j n 0 2n 1 p n x p n y p n z q n n

noncommutative reproducing kernel hilbert spaces abstract the theory of positive kernels and associated reproducing kernel hilbert spaces especially in the setting of holomorphic functions has been an important tool for the last several decades in a number of areas of complex analysis and operator theory an interesting generalization of holomorphic functions namely free noncommutative functions e g functions of square matrix arguments of arbitrary size satisfying additional natural compatibility conditions is now an active area of research with motivation and applications from a variety of areas e g noncommutative functional calculus free probability and optimization theory in linear systems engineering the purpose of this article is to develop a theory of positive kernels and associated reproducing kernel hilbert spaces for the setting of free noncommutative function theory

on the morita equivalence of tensor algebras our objective is two fold first we want to develop a notion of morita equivalence for c correspondences that guarantees that if two c correspondences e and f are morita equivalent then the tensor algebras of e and f taoeu and taofu are strongly morita equivalent in the sense of 8 the toeplitz algebras toeu and tofu are strongly morita equivalent in the sense of rieffel 32 see 33 also and the cuntz pimsner algebras 28 ooeu and oofu are strongly morita equivalent in the same sense we were inspired by earlier work of curto williams and the first author in 15 and combes 14 these papers investigate conditions implying that the crossed product of two c dynamical systems are strongly morita equivalent given that the coefficient algebras are strongly morita equivalent abadie eilers and exel 1 were similarly inspired and developed a theory of morita equivalence for special c correspondences our analysis extends theirs but our arguments are different see example 2 5 and remarks 3 3 and 3 6 for a comparison of their results and ours second we want to investigate the converse implication that is we study the following question if taoeu and taofu are strongly morita equivalent in the sense of 8 when are e and f morita equivalent in the sense we define for this converse direction we focus on the tensor algebras rather than the toeplitz and cuntz pimsner algebras because very little can be said in the self adjoint setting here we were inspired by arveson s paper 2 in which it is proved that two ergodic measure preserving transformations are conjugate if and only if certain non self adjoint crossed products associated with the transformations are algebraically isomorphic see 3 also his analysis was further extended by k saito and the first author to cover non self adjoint crossed products built from automorphisms of general von neumann algebras they showed that non self adjoint crossed products built from properly outer automorphisms of von neumann algebras are isomorphic if and only if the automorphisms are conjugate see 22 and 23 our principal result in the converse direction theorem 7 2 asserts that if e and f are two aperiodic correspondences and if taoeu is strongly morita equivalent to taofu in the sense of 8 then e and f are morita equivalent as we shall see in 5 the notion of aperiodicity is an exact analogue for correspondences of the concept of free action in ergodic theory free action was a central hypothesis in arveson s

poisson transforms on some c algebras generated by isometries abstract a noncommutative poisson transform associated to a certain class of sequences of operators on hilbert spaces with property p is defined on some universal c algebras resp nonselfadjoint algebras generated by isometries its properties are described and used to study these universal algebras and their representations as consequences we obtain a functional calculus isometric resp unitary dilations and commutant lifting theorem for the class of sequences of operators with property p our geometrical approach leads also to new and elementary proofs as well as extensions of some classical results

sums of products of ultraspherical functions analytical expressions for the sum n 0 n n 1 n 2 2 c n x c n y c n z d n u are given where c n and d n are ultraspherical polynomials and functions of the second kind respectively on the sets x y z 1 and x y z u 1

velocity measurements in a three dimensional compressible base flow the velocity field in the base region of a circular cylinder with a length to radius ratio of 3 0 aligned at a 10 deg angle of attack to a nominal mach 2 5 freestream has been investigated experimentally the objective is to better understand the mechanisms that govern the characteristics and development of three dimensional compressible base flows laser doppler velocimetry was used to measure both mean velocity components and turbulence statistics

closed analytical expressions for some useful sums and integrals involving legendre functions abstract simple closed analytical expressions are obtained for some integrals and infinite sums involving legendre functions the results are believed to be new these sums and integrals may be useful for the calculation of magnetic fields with configurations close to the toroidal ones the standard results of various asymptotic limits are recovered

reflexivity of non commutative hardy algebras abstract let h e be a non commutative hardy algebra associated with a w correspondence e these algebras were introduced in 2004 by muhly and solel and generalize the classical hardy algebra of the unit disc h d as a special case one obtains also the algebra f d of popescu which is h c d in our setting in this paper we view the algebra h e as acting on a hilbert space via an induced representation we write it h e and we study the reflexivity of h e this question was studied by arias and popescu in the context of the algebra f d and by other authors in several other special cases as it will be clear from our work the extension to the case of a general w correspondence e over a general w algebra m requires new techniques and approach we obtain some partial results in the general case and we turn to the case of a correspondence over a factor under some additional assumptions on the representation m b h we show that h e is reflexive then we apply these results to analytic crossed products h m and obtain their reflexivity for any automorphism aut m whenever m is a factor finally we show also the reflexivity of the compression of the hardy algebra to a suitable coinvariant subspace m which may be thought of as a generalized symmetric fock space