derivations vanishing on s lets be the group of finite permutations on countably many symbols we exhibit an embedding ofs into a uhf algebra mathfrak a of glimm typen such that if is a derivation vanishing ons and satisfying 0 where is the unique trace on mathfrak a then admits an extension which is the generator of ac dynamics

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

unbounded derivations commuting with compact group actions ii abstract let be a closed derivation in a c algebra 21 which commuteswith an ergodic action of a compact group on 5 then generates a c dynamics of 91 similar results are obtained for non ergodic actions on abelianc algebras and on the algebra of compact operators 1 introduction in 9 sakai showed that a non zero closed derivation in c t commuting withtranslations is a constant multiple of the derivative following this it wasshown in 4 7 that if g is a locally compact group and is a closed derivationin c 0 g commuting with left translations by elements of g then is the generatorof a c dynamics i e strongly continuous one parameter group of automor phisms of c 0 g a like result holds for c 0 g h h a closed sub group of g provided that g is either separable or the projective limit of lie groups in thisnote we assume g is compact and we obtain similar results for an ergodic action ofg on an arbitrary c algebra theorem 2 1 and for an arbitrary action of g on anabelian c algebra theorem 3 2 or on the algebra of compact operators theorem 4 1 we refer to 1 3 9 for background on unbounded derivations in c algebras

non commutative moment problems we are concerned with two problems called the generalized moment problem gmp and the quantum moment problem qmp both problems can be considered as non commutative versions of the classical moment problem et g be a connected lie group and 7b e g the universal enveloping algebra of the lie algebra of g suppose f is a given linear functional on 7b e g and is a fixed unitary representation of g we then ask gmp when do there exist a unitary representation u of g and a cyclic c vector for u such that f x x 7b e g qmp when is f of the form f x trdv x x 7b e g where is an operator such that dv x is of trace class for every x 7b e g

full diversity high rate space time block codes from division algebras we present some general techniques for constructing full rank minimal delay rate at least one space time block codes stbcs over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras field extensions as well as using noncommutative division algebras of the rational field spl qopf embedded in matrix rings the first half of the paper deals with constructions using field extensions of spl qopf working with cyclotomic field extensions we construct several families of stbcs over a wide range of signal sets that are of full rank minimal delay and rate at least one appropriate for any number of transmit antennas we study the coding gain and capacity of these codes using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas we also present a method of constructing stbcs using noncyclotomic field extensions in the later half of the paper we discuss two ways of embedding noncommutative division algebras into matrices left regular representation and representation over maximal cyclic subfields the 4 spl times 4 real orthogonal design is obtained by the left regular representation of quaternions alamouti s 1998 code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it also we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the stbcs obtained from this construction another family of cyclic division algebras discovered by brauer 1933 is discussed and several examples of stbcs derived from each of these constructions are presented

the structure of a brownian bubble we examine local geometric properties of level sets of the brownian sheet and in particular we identify the asymptotic distribution of the area of sets which correspond to excursions of the sheet high above a given level in the neighborhood of a particular random point it is equal to the area of certain individual connected components of the random set s t b t b s whereb is a standard brownian motion andb is essentially a bessel process of dimension 3 this limit distribution is studied and in particular explicit formulas are given for the probability that a point belongs to a specific connected component and for the expected area of a component given the height of the excursion ofb t b s in this component these formulas are evaluated numerically and compared with the results from direct simulations ofb andb

unbounded derivations tangential to compact groups of automorphisms ii let g be a compact abelian group and an action of g on a c algebra u such that u u u 0 u for all g where u is the spectral subspace of u corresponding to the character on g derivations which are defined on the algebra uf of g finite elements are considered in the special case u 0 these derivations are characterized by a cocycle on g with values in the relative commutant of u in the multiplier algebra of u and these derivations are inner if and only if the cocycles are coboundaries and bounded if and only if the cocycles are bounded under various restrictions on g and properties of the cocycle are deduced which again give characterizations of in terms of decompositions into generators of one parameter subgroups of g and approximately inner derivations finally a perturbation technique is devised to reduce the case uf uf to the case uf uf and u 0 this is used to show that any derivation with d uf is wellbehaved and if furthermore g t1 and uf uf the closure of generates a one parameter group of automorphisms of u in the case g td d 2 3 finite and uf uf it is shown that extends to a generator of a group of automorphisms of the weak closure of u in any g covariant representation

generally dimensional and constellation expansion free space time block codes for qam with full diversity this correspondence presents new rate 1 space time block codes stbcs attending full diversity over every quadrature amplitude modulation qam constellation when the number of tx antennas is a power of two from the simulation results our design performs very closely to the quasi orthogonal code with constellation rotation over 4 qam and 16 qam in the case of four tx antennas over quasi static rayleigh fading channels moreover the proposed codes would not cause any constellation expansion over qam symbols in contrast with the quasi orthogonal codes with constellation rotations

analytic continuation of local representations of symmetric spaces we prove the following analytic continuation theorem which applies to any virtual representation of any symmetric space g k the problem of passing from the euclidean group to the poincare group appears first to have been addressed and solved this way by klein and landau let g be a lie group k a closed subgroup and an involutive automorphism with k as fixed point subgroup if g k m is the corresponding symmetric lie algebra we form g k im and let g denote the simply connected lie group with g as lie algebra we consider virtual representations of g on a fixed complex hilbert space h adopting the definitions due to j frohlich k osterwalder and e seiler in particular g 1 g possibly unbounded operators for g in a neighborhood of e in g we prove that every such continues analytically to a strongly continuous unitary representation of g on h our theorem extends results due to klein landau frohlich et al and others earlier for special cases previous results were known only for special g k and then only for certain

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

exact rates of convergence to brownian local time in this article we are mainly concerned with proving lower bounds on some uniform approximation schemes for the local timea of one dimensional brownian motion consequently this leads to many exact limit theorems for brownian local times the latter results are paul levy s occupation time approximation the downcrossing theorem and an intrinsic construction

lie algebras of unbounded derivations abstract in this paper some new results on analytic domination of operators and on integrability of lie algebras of operators are proved and then our methods are applied to the study of lie algebras of unbounded derivations in c algebras

geography of the level sets of the brownian sheet we describe geometric properties of w wherew is a standard real valued brownian sheet in the neighborhood of the first hitp of the level set w along a straight line or smooth monotone curvel in such a neighborhood we use a decomposition of the formw s t b s b t x s t whereb s andb t are particular diffusion processes andx s t is comparatively small to show thatp is not on the boundary of any connected component of w rather components of this set form clusters nearp an integral test for thorn shaped neighborhoods ofl with tip atp that do not meet w is given we then analyse the position and size of clusters and individual connected components of w near such a thorn giving upper bounds on their height width and the space between clusters this provides a local picture of the level set our calculations are based on estimates of the length of excursions ofb andb and an accounting of the error termx

anticommuting selfadjoint operators abstract several equivalent definitions of anticommutativity for selfadjoint operators are presented it is shown that the anticommutativity of two selfadjoint operators a and b satisfying af bg bf ag 0 for all and g in the intersection of the domains of a and b is equivalent to the selfadjointness of their sum and difference in studying the structure of anticommuting selfadjoint operators a and b attention may be restricted to the case where both a and b are injective in that case a is unitarily equivalent to a moreover a and b are uniquely determined by a triplet b p q where b is unitary and p and q are commuting injective positive and selfadjoint operators this is a natural correspondence

the sharp markov property of the brownian sheet and related processes keywords brownian sheet sharp markov property processes with independent planar increments reference prob article 1992 001doi 10 1007 bf02392978 record created on 2008 12 01 modified on 2017 05 12

derivations commuting with abelian gauge actions on lattice systems let be an action of a compact abelian groupg on ac algebraa and assume that the fixed point subalgebraa is an af algebra we show that if is a closed derivation ona commuting with and the restriction of toa generates a one parameter group of automorphisms then itself is a generator in particular the result applies if is an infinite product action ofg on a uhf algebra furthermore if in this situation 1 and 2 are two derivations both satisfying the hypotheses on and 1 and 2 have the same restriction toa then there exists a one parameter subgroup of the action with generator 0 such thatd 1 d 2 d 0 is a joint core for the three derivations and 2 1 0 on this core

eccentric behaviors of the brownian sheet along lines keywords brownian sheet level sets points of increase reference prob article 2002 001view record in web of science record created on 2008 12 01 modified on 2017 05 12

unbounded derivations commuting with compact group actions let be a closed derivation in ac algebra mathfrak a which commutes with an ergodic action of a compact group on mathfrak a then generates ac dynamics of mathfrak a similar results are obtained for non ergodic actions on abelianc algebras and on the algebra of compact operators

signal constellations for quasi orthogonal space time block codes with full diversity space time block codes stbcs from orthogonal designs proposed by alamouti and tarokh jafarkhani calderbank have attracted considerable attention lately due to their fast maximum likelihood ml decoding and full diversity however the maximum symbol transmission rate of an stbc from complex orthogonal designs for complex signals is only 3 4 for three and four transmit antennas and it is difficult to construct complex orthogonal designs with rate higher than 1 2 for more than four transmit antennas recently jafarkhani tirkkonen boariu hottinen and papadias foschini proposed stbcs from quasi orthogonal designs where the orthogonality is relaxed to provide higher symbol transmission rates with the quasi orthogonal structure the quasi orthogonal stbcs still have a fast ml decoding but do not have the full diversity the performance of these codes is better than that of the codes from orthogonal designs at low signal to noise ratio snr but worse at high snr this is due to the fact that the slope of the performance curve depends on the diversity it is desired to have the quasi orthogonal stbcs with full diversity to ensure good performance at high snr in this paper we achieve this goal by properly choosing the signal constellations specifically we propose that half of the symbols in a quasi orthogonal design are chosen from a signal constellation set a and the other half of them are chosen from a rotated constellation e sup j spl phi a the resulting stbcs can guarantee both full diversity and fast ml decoding moreover we obtain the optimum selections of the rotation angles spl phi for some commonly used signal constellations simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high snrs

on the distribution of bubbles of the brownian sheet let w be a real valued two parameter brownian sheet let us define n t h to be the total number of bubbles of w in 0 t 2 whose maximum height is greater than h evidently lim h 0 n t h and lim t n t h it is the goal of this paper to provide fairly accurate estimates on n t h both as t and as h 0 loosely speaking we show that there are of order h 3 many such bubbles as h 0 and t 3 many as t

analytic vectors and integrability of lie algebra representations abstract we prove that a representation of a finite dimensional lie algebra in a banach space is integrable if it admits a suitable invariant set of analytic vectors

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

diagonal algebraic space time block codes we construct a new family of linear space time st block codes by the combination of rotated constellations and the hadamard transform and we prove them to achieve the full transmit diversity over a quasi static or fast fading channels the proposed codes transmit at a normalized rate of 1 symbol s when the number of transmit antennas n 1 2 or n is a multiple of four we spread a rotated version of the information symbol vector by the hadamard transform and send it over n transmit antennas and n time periods for other values of n we construct the codes by sending the components of a rotated version of the information symbol vector over the diagonal of an n spl times n st code matrix the codes maintain their rate diversity and coding gains for all real and complex constellations carved from the complex integers ring z i and they outperform the codes from orthogonal design when using complex constellations for n 2 the maximum likelihood ml decoding of the proposed codes can be implemented by the sphere decoder at a moderate complexity it is shown that using the proposed codes in a multiantenna system yields good performances with high spectral efficiency and moderate decoding complexity