commuting difference operators with elliptic coefficients from baxter s vacuum vectors for quantum integrable models with elliptic r matrix we construct the baxter q operator in infinite dimensional representations of the algebra of observables

admm based fast algorithm for multi group multicast beamforming in large scale wireless systems multi group multicast beamforming in wireless systems with large antenna arrays and massive audience is investigated in this paper multicast beamforming design is a well known non convex quadratically constrained quadratic programming qcqp problem a conventional method to tackle this problem is to approximate it as a semi definite programming problem via semi definite relaxation whose performance however deteriorates considerably as the number of per group users goes large a recent attempt is to apply convex concave procedure ccp to find a stationary solution by treating it as a difference of convex programming problem whose complexity however increases dramatically as the problem size increases in this paper we propose a low complexity high performance algorithm for multi group multicast beamforming design in large scale wireless systems by leveraging the alternating direction method of multipliers admm together with ccp in specific the original non convex qcqp problem is first approximated as a sequence of convex subproblems via ccp each convex subproblem is then reformulated as a novel admm form our admm reformulation enables that each updating step is performed by solving multiple small size subproblems with closed form solutions in parallel numerical results show that our fast algorithm maintains the same favorable performance as state of the art algorithms but reduces the complexity by orders of magnitude

bohr inequalities for free holomorphic functions on polyballs abstract multivariable operator theory is used to provide bohr inequalities for free holomorphic functions with operator coefficients on the regular polyball b n n n 1 n k n k which is a noncommutative analogue of the scalar polyball c n 1 1 c n k 1 the bohr radius k m h b n resp k h b n associated with the multi homogeneous resp homogeneous power series expansions of the free holomorphic functions are the main objects of study in this paper we extend a theorem of bombieri and bourgain for the disc d z c z 1 to the polyball and obtain the estimations 1 3 k k m h b n 2 log k k if k 1 extending boas khavinson result for the scalar polydisc d k with respect to the homogeneous power series expansion we prove that k h b n 1 3 extending the classical result and obtain analogues of caratheodory fejer and egervary szasz inequalities for free holomorphic functions with operator coefficients and positive real parts on the polyball these results are used to provide multivariable analogues of landau s inequality and bohr s inequality when the norm is replaced by the numerical radius of an operator when specialized to the regular polydisc d k which corresponds to the case n 1 n k 1 we obtain new results concerning bohr landau fejer and harnack inequalities for operator valued holomorphic functions and k pluriharmonic functions on the scalar polydisc d k the results of the paper can be used to obtain bohr type inequalities for the noncommutative ball algebra a n the hardy algebra f n and the c algebra c s generated by the universal model s of the polyball b n

multiple rademacher means and their applications abstract we evaluate multiple rademacher means for various classes of multilinear operators under the assumption that the range has cotype q these results show that the class of multiple q 2 summing operators plays an important role further we get new extensions of bu s theorem in the multilinear case

there exist multilinear bohnenblust hille constants cn n 1 with limn cn 1 cn 0 abstract the n linear bohnenblust hille inequality asserts that there is a constant c n 1 such that the l 2 n n 1 norm of u e i 1 e i n i 1 i n 1 n is bounded above by c n times the supremum norm of u for any n linear form u c n c n c and n n the same holds for real scalars we prove what we call fundamental lemma which brings new information on the optimal constants k n n 1 for both real and complex scalars for instance k n 1 k n 0 87 n 0 473 for infinitely many n s for complex scalars we give a formula of surprisingly low growth in which e and the famous euler mascheroni constant appear k n 1 4 1 e 2 1 2 j 1 n 1 j log 2 e 2 1 2 1 n 2 we study the interplay between the kahane salem zygmund and the bohnenblust hille polynomial and multilinear inequalities and provide estimates for bohnenblust hille type inequality constants for any exponent q 2 n n 1

a subexponential vector valued bohnenblust hille type inequality abstract bayart pellegrino and seoane recently proved that the polynomial bohnenblust hille inequality for complex scalars is subexponential we show that a vector valued polynomial bohnenblust hille inequality on complex banach lattices is also subexponential for some special cases our main result recovers the best known constants of the classical polynomial inequality provided in 4

banach spaces of general dirichlet series abstract we study when the spaces of general dirichlet series bounded on a half plane are banach spaces and show that some of those classes are isometrically isomorphic between themselves in a precise way let n be a strictly increasing sequence of positive real numbers such that lim n n we denote by h n the complex normed space of all dirichlet series d s n b n n s which are convergent and bounded on the half plane re s 0 endowed with the norm d sup re s 0 d s if there exists q 0 such that inf n n 1 q n q 0 then h n is a banach space further if there exists a strictly increasing sequence r n of positive numbers such that the sequence log r n is q linearly independent n r for n p and n is the increasing rearrangement of the sequence n then h n is isometrically isomorphic to h b c 0 with this condition we explain more explicitly the optimal cases of the difference among the abscissas c b u and a

generalization of a theorem of bohr for bases in spaces of holomorphic functions of several complex variables abstract in the first part we generalize the classical result of bohr by proving that an analogous phenomenon occurs whenever d is an open domain in c m or more generally a complex manifold and n n 0 is a basis in the space of holomorphic functions h d such that 0 1 and n z0 0 n 1 for some z0 d namely then there exists a neighborhood u of the point z0 such that whenever a holomorphic function on d has modulus less than 1 the sum of the suprema in u of the moduli of the terms of its expansion is less than 1 too in the second part we consider some natural hilbert spaces of analytic functions and derive necessary and sufficient conditions for the occurrence of bohr s phenomenon in this setting

discrete skew selfadjoint canonical systems and the isotropic heisenberg magnet model abstract a discrete analog of a skew self adjoint canonical zakharov shabat or akns system with a pseudo exponential potential is introduced for the corresponding weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices as an application explicit solutions are obtained for the discrete integrable nonlinear equation corresponding to the isotropic heisenberg magnet model state space techniques from mathematical system theory play an important role in the proofs

the periodic toda chain and a matrix generalization of the bessel function recursion relations the authors obtain the quantization conditions of the periodic toda lattice in the baxter form lambda u q u inq u i i nq u i lambda is the transfer matrix containing the information about the spectrum and q is an integral operator commuting with lambda the logarithms of the matrix elements of q are the generating functions of the canonical backlund transformation the requirement that q is analytic and vanishes when u goes to infinity completely determines the spectrum of lambda

multiple summing operators on banach spaces abstract in this paper we improve some previous results about multiple p summing multilinear operators by showing that every multilinear form from l 1 spaces is multiple p summing for 1 p 2 the proof is based on the existence of a predual for the banach space of multiple p summing multilinear forms we also show the failure of the inclusion theorem in this class of operators and improve some results of y melendez and a tonge about dominated multilinear operators

baxter s q operator for the homogeneous xxx spin chain applying the pasquier gaudin procedure we construct baxter s q operator for the homogeneous xxx model as an integral operator in the standard representation of sl 2 the connection between the q operator and the local hamiltonians is discussed we show that lipatov s duality symmetry operator arises naturally as the leading term of the asymptotic expansion of the q operator for large values of the spectral parameter

consensus admm for general quadratically constrained quadratic programming nonconvex quadratically constrained quadratic programming qcqp problems have numerous applications in signal processing machine learning and wireless communications albeit the general qcqp is np hard and several interesting special cases are np hard as well this paper proposes a new algorithm for general qcqp the problem is first reformulated in consensus optimization form to which the alternating direction method of multipliers can be applied the reformulation is done in such a way that each of the subproblems is a qcqp with only one constraint qcqp 1 which is efficiently solvable irrespective of non convexity the core components are carefully designed to make the overall algorithm more scalable including efficient methods for solving qcqp 1 memory efficient implementation parallel distributed implementation and smart initialization the proposed algorithm is then tested in two applications multicast beamforming and phase retrieval the results indicate superior performance over prior state of the art methods

coordinatewise multiple summing operators in banach spaces we invent the new notion of coordinatewise multiple summing operators in banach spaces and use it to study various vector valued extensions of the well know bohnenblust hille inequality which originally extended littlewood s 4 3 inequality our results have application on the summability of monomial coefficients of m homogeneous polynomials p l lp as well as for the convergence theory of products of vector valued dirichlet series

a q difference baxter operator for the ablowitz ladik chain we construct the baxter operator and the corresponding baxter equation for a quantum version of the ablowitz ladik model the result is achieved in two different ways by using the well known bethe ansatz technique and by looking at the quantum analogue of the classical backlund transformations general results about integrable models governed by the same r matrix algebra will be given baxter s equation comes out to be a q difference equation involving both the trace and the quantum determinant of the monodromy matrix the spectrality property of the classical backlund transformations gives a trace formula representing the classical analogue of baxter s equation a q integral representation of the baxter operator is discussed

separation of variables for the ruijsenaars model and a new integral representation for the macdonald polynomials using the baker akhiezer function technique we construct a separation of variables for the classical trigonometric three particle ruijsenaars model a relativistic generalization of the calogero moser sutherland model in the quantum case an integral operator m is constructed from the askey wilson contour integral the operator m transforms the eigenfunctions of the commuting hamiltonians the macdonald polynomials for the root sytem into the factorized form where s y is a laurent polynomial of one variable expressed in terms of the basic hypergeometric series the inversion of m produces a new integral representation for the macdonald polynomials we also present some results and conjectures for the general n particle case

sharp bohr type inequality abstract this article is devoted to the sharp improvement of the classical bohr inequality for bounded analytic functions defined on the unit disk we also prove two other sharp versions of the bohr inequality by replacing the constant term by the absolute of the function and the square of the absolute of the function respectively

asymptotics of the bohr radius for polynomials of fixed degree we obtain a characterization and conjecture asymptotics of the bohr radius for the class of complex polynomials in one variable our work is based on the notion of bound preserving operators

factorization of absolutely continuous polynomials abstract in this paper we study the ideal of dominated p continuous polynomials that extend the nowadays well known ideal of p dominated polynomials to the more general setting of the interpolated ideals of polynomials we give the polynomial version of pietsch s factorization theorem for this new ideal although based on botelho et al in press 16 our factorization theorem requires new techniques inspired in the theory of banach lattices

baxterization of glq 2 and its application to the liouville model and some other models on a lattice we develop the baxterization approach to an extension of the quantum group gl q 2 we introduce two matrices which play the role of spectral parameter dependent l matrices and observe that they are naturally related to two different comultiplications using these comultiplication structures we find the related fundamental r operators in terms of powers of coproducts and also give their equivalent forms in terms of quantum dilogarithms the corresponding quantum local hamiltonians are given in terms of logarithms of positive operators an analogous construction is developed for the q oscillator and weyl algebras using the fact that their algebraic and coalgebraic structures can be obtained as reductions of those for the quantum group as an application the lattice liouville model the q dst model the volterra model a lattice regularization of the free field and the relativistic toda model are considered

factorization of the transfer matrices for the quantum sl 2 spin chains and baxter equation it is shown that the transfer matrices of homogeneous sl 2 invariant spin chains with generic spin both closed and open are factorized into the product of two operators the latter satisfy the baxter equation that follows from the structure of the reducible representations of the sl 2 algebra

on baxter q operators for the toda chain we suggest a procedure for the construction of baxter q operators for the toda chain apart from the one parametric family of q operators considered in our recent paper pronko 2000 commun math phys to appear we also give the method of construction of two basic q operators and the derivation of the functional relations for these operators also we have found the relation of the basic q operators with bloch solutions of the quantum linear problem

a new multilinear insight on littlewood s 4 3 inequality abstract we unify littlewood s classical 4 3 inequality a forerunner of grothendieck s inequality together with its m linear extension due to bohnenblust and hille which originally settled bohr s absolute convergence problem for dirichlet series with a scale of inequalties of bennett and carl in l p spaces which are of fundamental importance in the theory of eigenvalue distribution of power compact operators as an application we give estimates for the monomial coefficients of homogeneous l p valued polynomials on c 0

separation of variables and backlund transformations for the symmetric lagrange top we construct the one and two point integrable maps backlund transformations for the symmetric lagrange top we show that the lagrange top has the same algebraic poisson structure that belongs to the sl 2 gaudin magnet the two point map leads to a real time discretization of the continuous flow therefore it provides an integrable numerical scheme for integrating the physical flow we illustrate the construction by a few pictures of the discrete flow calculated in matlab

multipliers of dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables let mathscr h infty be the set of all ordinary dirichlet series d sum n a n n s representing bounded holomorphic functions on the right half plane a completely multiplicative sequence b n of complex numbers is said to be an ell 1 multiplier for mathscr h infty whenever sum n a n b n infty for every d in mathscr h infty we study the problem of describing such sequences b n in terms of the asymptotic decay of the subsequence b p j where p j denotes the jth prime number given a completely multiplicative sequence b b n we prove among other results b is an ell 1 multiplier for mathscr h infty provided b p j 1 for all j and overline lim n frac 1 log n sum j 1 n b p j 2 1 and conversely if b is an ell 1 multiplier for mathscr h infty then b p j 1 for all j and overline lim n frac 1 log n sum j 1 n b p j 2 le 1 here b stands for the decreasing rearrangement of b following an ingenious idea of harald bohr it turns out that this problem is intimately related with the question of characterizing those sequences z in the infinite dimensional polydisk mathbb d infty the open unit ball of ell infty for which every bounded and holomorphic function f on mathbb d infty has an absolutely convergent monomial series expansion sum alpha frac partial alpha f 0 alpha z alpha moreover we study analogous problems in hardy spaces of dirichlet series and hardy spaces of functions on the infinite dimensional polytorus mathbb t infty

backlund transformations for the sl 2 gaudin magnet elementary one and two point backlund transformations are constructed for the generic case of the sl 2 gaudin magnet the spectrality property is used to construct these explicitly given poisson integrable maps which are time discretizations of the continuous flows with any hamiltonian from the spectral curve of the 2 2 lax matrix

orthogonal confluent hypergeometric lattice polynomials here is a method of solving the difference differential equations of the confluent hypergeometric differential equation using a generalized pochhammer matrix product this method provides a convenient analytical way to relate various solutions of the confluent hypergeometric function to each other when their parameters fall on the same point lattice these solutions also are of interest to the general classification of orthogonal polynomials and the metrics used to generate them this method generates laurent polynomials over the complex domain that are an orthogonal system utilizing a 2 2 matrix weight function where the weight matrix has elements that are products of a kummer solution and its derivative the index incremented pochhammer matrix polynomials obey a 4 4 system of differential equations with a frobenius solution involving non commuting matrices that also extends these results to non integer values but with infinite laurent series the termination condition for a polynomial series in the midst of infinite series sheds light on solving general systems of regular linear differential equations the differential equations generalize heun s double confluent equation with matrix coefficients for a radiative transfer flux integral there is a distinct advantage of using these lattice polynomials compared to an asymptotic series power series combination we conjecture similar convergence properties for evaluations of confluent hypergeometric functions of either kind and that these matrix methods can be extended to gauss hypergeometric functions and generalized hypergeometric functions

unconditional basis and gordon lewis constants for spaces of polynomials abstract no infinite dimensional banach space x is known which has the property that for m 2 the banach space of all continuous m homogeneous polynomials on x has an unconditional basis following a program originally initiated by gordon and lewis we study unconditionality in spaces of m homogeneous polynomials and symmetric tensor products of order m in banach spaces we show that for each banach space x which has a dual with an unconditional basis x i the approximable nuclear m homogeneous polynomials on x have an unconditional basis if and only if the monomial basis with respect to x i is unconditional moreover we determine an asymptotically correct estimate for the unconditional basis constant of all m homogeneous polynomials on l n p and use this result to narrow down considerably the list of natural candidates x with the above property

on summability of nonlinear mappings a new approach the main goal of this paper is to characterize arbitrary nonlinear non multilinear mappings f x 1 times cdots times x n rightarrow y between banach spaces that satisfy a quite natural pietsch domination type theorem around a given point a 1 ldots a n in x 1 times cdots times x n as a consequence of our approach a notion of weighted summability arises naturally which may be an interesting topic for further investigation

a τ function on the inhomogeneous lattice and the classical isotropic heisenberg spin chain a function on the inhomogeneous lattice is introduced by a deformation of that of the toda lattice hierarchy an associated discrete time integrable system is constructed in sato and lax formalisms it is shown that a one dimensional reduction of the system gives a backlund transformation of the classical isotropic heisenberg spin chain which is equivalent to the rii chain proposed by spiridonov and zhedanov

bohr s strip for vector valued dirichlet series bohr showed that the width of the strip in the complex plane on which a given dirichlet series sum a n n s s in mathbb c converges uniformly but not absolutely is at most 1 2 and bohnenblust hille that this bound in general is optimal we prove that for a given infinite dimensional banach space y the width of bohr s strip for a dirichlet series with coefficients an in y is bounded by 1 1 cot y where cot y denotes the optimal cotype of y this estimate even turns out to be optimal and hence leads to a new characterization of cotype in terms of vector valued dirichlet series

reinhardt domains of holomorphy in banach spaces abstract it is known that in c 0 the holomorphic functions representable by multiple power series the series of monomials are those of nuclear type in this article we show that in a banach space with unconditional schauder basis every domain of existence is the domain of existence of a holomorphic function representable by a multiple power series and in fact the domain of convergence of such a series

summing multilinear operators by blocks the isotropic and anisotropic cases abstract unifying several directions of the development of the study of summing multilinear operators between banach spaces we construct a general framework that studies under one single definition multilinear operators that are summing with respect to sums taken over any number of indices iterated and non iterated sums the isotropic and the anisotropic cases sums over arbitrary blocks and over several different sequence norms a large number of special classes of multilinear operators and of methods of generating classes of multilinear operators are recovered as particular instances ideal properties and coincidence theorems for the general classes are proved

high performance adaptive algorithms for single group multicast beamforming the single group multicast beamforming problem is np hard and the available approximations do not always achieve favorable performance complexity tradeoffs this paper introduces a new class of adaptive multicast beamforming algorithms that features guaranteed convergence and state of the art performance at low complexity each update takes a step in the direction of an inverse signal to noise ratio snr weighted linear combination of the snr gradient vectors of all the users convergence of this update to a karush kuhn tucker kkt point of proportionally fair beamforming is established simulations show that the proposed approach can enable better performance than the prior state of art in terms of multicast rate at considerably lower complexity this reveals an interesting link between max min fair and proportionally fair multicast beamforming formulations for cases where there is no initial channel state information at the transmitter an online algorithm is developed that simultaneously learns the user channel correlation matrices and adapts the beamforming vector to maximize the minimum long term average snr among the users using only periodic binary snr feedback from each receiver the online algorithm uses the analytic center cutting plane method to quickly learn the user correlation matrices with limited signaling overhead

volume estimates in spaces of homogeneous polynomials given m we derive upper and lower estimates for the volume of the unit ball of the banach space mathcal p m e n all m homogeneous polynomials defined on the nth section e n of a symmetric banach sequence space e with constants depending on m only we apply this result to obtain asymptotically correct orders of various important invariants of mathcal p m e n from local banach space theory as e g volume ratios cotype and type 2 constants projection constants or banach mazur distances

integrable structure of conformal field theory ii q operator and ddv equation this paper is a direct continuation of 1 where we began the study of the integrable structures in conformal field theory we show here how to construct the operators bf q pm lambda which act in the highest weight virasoro module and commute for different values of the parameter these operators appear to be the cft analogs of the q matrix of baxter 2 in particular they satisfy baxter s famous t q equation we also show that under natural assumptions about analytic properties of the operators as the functions of the baxter s relation allows one to derive the nonlinear integral equations of destri de vega ddv 3 for the eigenvalues of the q operators we then use the ddv equation to obtain the asymptotic expansions of the q operators at large it is remarkable that unlike the expansions of the t operators of 1 the asymptotic series for q contains the dual nonlocal integrals of motion along with the local ones we also discuss an intriguing relation between the vacuum eigenvalues of the q operators and the stationary transport properties in the boundary sine gordon model on this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum hall system

the bohnenblust hille inequality for homogeneous polynomials is hypercontractive the bohnenblust hille inequality says that the 2m m 1 norm of the coefcients of an m homogeneous polynomial p on c n is bounded by kpk1 times a constant independent of n wherekk 1 denotes the supremum norm on the polydisc d n the main result of this paper is that this inequality is hypercontractive i e the constant can be taken to be c m for some c 1 combining this improved version of the bohnenblust hille inequality with other results we obtain the following the bohr radius for the polydisc d n behaves asymptotically as p logn n modulo a factor bounded away from 0 and innity

on the quantum inverse scattering method for the dst dimer abstract the quantum inverse scattering method is used to solve the spectral problem of the discrete self trapping dimer in the case of both a quadratic and a linear r matrix algebra representation the first case is solved by the algebraic bethe ansatz while in the case of the linear r matrix algebra we use the method of separation of variables in this last case it is shown that the wave functions of the quantum discrete self trapping dimer are related to the solutions of a heun s type equation and that the system is equivalent to the two site hyperbolic gaudin magnet separable in elliptic coordinates

quantum backlund transformation for the integrable dst model for the integrable case of the discrete self trapping dst model we construct a backlund transformation the dual lax matrix and the corresponding dual backlund transformation are also found and studied the quantum analogue of the backlund transformation q operator is constructed as the trace of a monodromy matrix with an infinite dimensional auxiliary space we present the q operator as an explicit integral operator as well as describing its action on the monomial basis as a result we obtain a family of integral equations for multivariable polynomial eigenfunctions of the quantum integrable dst model these eigenfunctions are special functions of the heun class which is beyond the hypergeometric class the integral equations found are new and they shall provide a basis for efficient analytical and numerical studies of such complicated functions

on backlund transformations for many body systems using the n particle periodic toda lattice and the relativistic generalization due to ruijsenaars of the elliptic calogero moser system as examples we revise the basic properties of the backlund transformations bts from the hamiltonian point of view the analogy between the bt and baxter s quantum q operator pointed out by pasquier and gaudin is exploited to produce a conjugated variable for the parameter of the bt such that belongs to the spectrum of the lax operator as a consequence the generating function of the composition of n bts gives rise to another canonical transformation separating variables for the model for the toda lattice the dual bt parametrized by is introduced

convergence of dirichlet polynomials in banach spaces both authors were supported by the mec project mtm2008 03211 the second author was partially supported by grants pr2007 0384 mec and upv paid 00 07

bohr radii of vector valued holomorphic functions abstract motivated by the scalar case we study bohr radii of the n dimensional polydisc d n for holomorphic functions defined on d n with values in banach spaces

let s baxterise we recall the concept of baxterisation of an r matrix or of a monodromy matrix which corresponds to build from one point in the r matrix parameter space the algebraic variety where the spectral parameter s live we show that the baxterisation which amounts to studying the iteration of a birational transformation is a win win strategy it enables to discard efficiently the non integrable situations focusing directly on the two interesting cases where the algebraic varieties are of the so called general type finite order iteration or are abelian varieties infinite order iteration we emphasize the heuristic example of the sixteen vertex model and provide a complete description of the finite order iterations situations for the baxter model we show that the baxterisation procedure can be introduced in much larger frameworks where the existence of some underlying yang baxter structure is not used we baxterise l operators local quantum lax matrices and quantum hamiltonians

a family of the poisson brackets compatible with the sklyanin bracket we introduce a family of compatible poisson brackets on the space of 2 2 polynomial matrices which contains the sklyanin bracket and use it to derive a multi hamiltonian structure for a set of integrable systems that includes the xxx heisenberg magnet the open and periodic toda lattices the discrete self trapping model and the goryachev chaplygin gyrostat

reverse inclusions for multiple summing operators abstract multiple summing operators have been proven to be useful in several areas of analysis and mathematical physics in this paper we prove reverse inclusions for this class of operators completing the work already initiated in d perez garcia the inclusion theorem for multiple summing operators studia math 165 3 2004 275 290

type and cotype of musielak orlicz sequence spaces let n be a musielak orlicz function and l the musielak orlicz sequence space generated by it is shown that satisfies condition qiff is equivalent to aq concave function n it is also proved thatl is of cotypeq typep if and only if satisfies condition q 2and pconditions respectively as applications we obtain characterization of the type and cotype of various sequence spaces nakano weighted orlicz and orlicz sequence spaces furthermore a relation betweenq concavity p convexity lowerq estimate upperp estimate and cotype type of l is given

some polynomial versions of cotype and applications abstract we introduce non linear versions of the classical cotype of banach spaces we show that spaces with l u st and cotype and spaces having fourier cotype enjoy our non linear cotype we apply these concepts to get results on convergence of vector valued power series in infinite many variables and on l 1 multipliers of vector valued dirichlet series finally we introduce cotype with respect to indexing sets an idea that includes our previous definitions

weighted fair multicast multigroup beamforming under per antenna power constraints a multiantenna transmitter that conveys independent sets of common data to distinct groups of users is considered this model is known as physical layer multicasting to multiple cochannel groups in this context the practical constraint of a maximum permitted power level radiated by each antenna is addressed the per antenna power constrained system is optimized in a maximum fairness sense with respect to predetermined quality of service weights in other words the worst scaled user is boosted by maximizing its weighted signal to interference plus noise ratio a detailed solution to tackle the weighted max min fair multigroup multicast problem under per antenna power constraints is therefore derived the implications of the novel constraints are investigated via prominent applications and paradigms what is more robust per antenna constrained multigroup multicast beamforming solutions are proposed finally an extensive performance evaluation quantifies the gains of the proposed algorithm over existing solutions and exhibits its accuracy over per antenna power constrained systems

baxter t q equation for shape invariant potentials the finite gap potentials case the darboux transformation applied recurrently on a schrodinger operator generates what is called a dressing chain or from a different point of view a set of supersymmetric shape invariant potentials the finite gap potential theory is a special case of the chain for the finite gap case the equations of the chain can be expressed as a time evolution of a hamiltonian system we apply sklyanin s method of separation of variables to the chain we show that the classical equation of the separation of variables is the baxter t q relation after quantization