ofdm based on low complexity transform to increase multipath resilience and reduce papr this paper introduces a new multicarrier system using a low computational complexity transform that combines the walsh hadamard transform wht and the discrete fourier transform dft into a single fast orthonormal unitary transform the proposed transform is used in a new orthogonal frequency division multiplexing t ofdm system leading to a significant improvement in bit error rate ber and reasonable reduction in the peak to average power ratio papr use of the proposed transform with ofdm has been found to attain high frequency diversity gain by combining all data samples resulting in the transmission over many subcarriers consequently the detrimental effect arising from channel fading on the subcarrier power is minimized theoretical analysis of the uncoded t ofdm performance over additive white gaussian noise awgn flat fading quasi static fixed within the entire period of ofdm symbol transmission frequency selective fading channel models with zero forcing zf and minimum mean square error mmse equalizers is presented in this work moreover the low superposition of the subcarriers passing through the t transforms leads to a reduction in the high peak of the transmitted signal whilst preserving the average transmitted power and data rate analytical results confirmed by simulations demonstrated that the proposed t ofdm system achieves lower papr and the same ber over awgn and flat fading channels compared to ofdm t ofdm is found to have better ber when mmse equalizer is used but slightly worse when zf equalizer is used

one parameter groups of regular quasimultipliers abstract groups of unbounded operators are approached in the setting of the esterle quasimultiplier theory we introduce groups of regular quasimultipliers of growth or groups for short where is a continuous weight on the real line we study the relationship of groups with families of operators and homomorphisms such as regularized distribution and integrated groups holomorphic semigroups and functional calculi some convolution banach algebras of functions with derivatives to fractional order are needed which we construct using the weyl fractional calculus

gaussian heat kernel upper bounds via the phragmen lindelof theorem we prove that in presence of l gaussian estimates so called davies gaffney estimates on diagonal upper bounds imply precise off diagonal gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces

a comparison of pilot aided channel estimation methods for ofdm systems this paper deals with the estimation of the channel impulse response cir in orthogonal frequency division multiplexed ofdm systems in particular we focus on two pilot aided schemes the maximum likelihood estimator mle and the bayesian minimum mean square error estimator mmsee the advantage of the former is that it is simpler to implement as it needs no information on the channel statistics on the other hand the mmsee is expected to have better performance as it exploits prior information about the channel theoretical analysis and computer simulations are used in the comparisons at snr values of practical interest the two schemes are found to exhibit nearly equal performance provided that the number of pilot tones is sufficiently greater than the cirs length otherwise the mmsee is superior in any case the mmsee is more complex to implement

operator biflatness of the fourier algebra and approximate indicators for subgroups abstract we investigate if for a locally compact group g the fourier algebra a g is biflat in the sense of quantized banach homology a central role in our investigation is played by the notion of an approximate indicator of a closed subgroup of g the fourier algebra is operator biflat whenever the diagonal in g g has an approximate indicator although we have been unable to settle the question of whether a g is always operator biflat we show that for g sl 3 c the diagonal in g g fails to have an approximate indicator

spectral decompositions of isometries oncp the spatial action of the stone type spectral family for a certain type of strongly continuous one parameter groups of surjective isometries as well as of the spectral decomposition of their single elements oncp 1 p is examined the umd structure for 1 p and triangular truncations and duality forp 1 are involved in various cases concrete descriptions of the associated riesz nagy operators and arveson s spectral subspaces are derived as byproducts of independent interest

radial fourier multipliers of lp r2 abstract we give sufficient conditions in terms of differentiability and growth properties for a radial function to be an lp r2 fourier multiplier these conditions are in the nature of best possible

a separation property of positive definite functions on locally compact groups and applications to fourier algebras abstract for a closed subgroup h of a locally compact group g consider the property that the continuous positive definite functions on g which are identically one on h separate points in g h from points in h we prove a structure theorem for almost connected groups having this separation property for every closed subgroup also when a pair g h has this separation property there are interesting consequences in the ideal theory of the fourier algebra of g

distribution of inner product of complex gaussian random vectors and its applications let x and y be two independent l x 1 complex gaussian random vectors distributed as cn m 2 il and cn my y2 il respectively where i l denotes the l x l identity matrix the joint characteristic function c f of the real and imaginary parts of the inner product yh x is derived in closed form with h denoting the conjugate transpose based on this joint c f a unified analytical framework for the derivation of the average symbol error probability asep of a multibranch diversity reception system over flat correlated fading using m ary phase shift keying is developed the receiver employs maximal ratio combining with least squares channel estimation by means of pilot symbols the optimal average pilot to noise power ratio is obtained in closed form and the analytical framework is applied to nakagami and rice fading for nakagami fading closed form asep expressions are obtained for the cases of high signal to noise snr and binary phase shift keying while for rice fading high snr approximate expressions are obtained in terms of a single integral under the constant correlation model and for independent and identically distributed channels both analytical and computer simulation results are presented and compared in order to verify the validity of the proposed analysis

on the operator homology of the fourier algebra and its cb multiplier completion abstract we study various operator homological properties of the fourier algebra a g of a locally compact group g establishing the converse of two results of ruan and xu 35 we show that a g is relatively operator 1 projective if and only if g is in and that a g is relatively operator 1 flat if and only if g is inner amenable we also exhibit the first known class of groups for which a g is not relatively operator c flat for any c 1 as applications of our techniques we establish a hereditary property of inner amenability answer an open question of lau and paterson 24 and answer an open question of anantharaman delaroche 1 on the equivalence of inner amenability and property w in the bimodule setting we show that relative operator 1 biflatness of a g is equivalent to the existence of a contractive approximate indicator for the diagonal g in the fourier stieltjes algebra b g g thereby establishing the converse to a result of aristov runde and spronk 3 we conjecture that relative 1 biflatness of a g is equivalent to the existence of a quasi central bounded approximate identity in l 1 g that is g is qsin and verify the conjecture in many special cases we finish with an application to the operator homology of a c b g giving examples of weakly amenable groups for which a c b g is not operator amenable

nonharmonic fourier series and spectral theory we consider the problem of using functions g x exp ix 1 x to form biorthogonal expansions in the spaces lp 7r sr for various values of p the work of paley and wiener and of levinson considered conditions of the form ix ni a p which insure that g is part of a biorthogonal system and the resulting biorthogonal expansions are pointwise equiconvergent with ordinary fourier series norm convergence is obtained for p 2 in this paper rather than imposing an explicit growth condition we assume that x n is a multiplier sequence on lp t 7t conditions are given insuring that g inherits both norm and pointwise convergence properties of ordinary fourier series further xn and gn are shown to be the eigenvalues and eigenfunctions of an unbounded operator a which is closely related to a differential operator i a generates a strongly continuous group and a2 generates a strongly continuous semigroup half range expansions involving cos x x or sin x n x on 0 7t are also shown to arise from linear operators which generate semigroups many of these results are obtained using the functional calculus for well bounded operators

operator space structure and amenability for figa talamanca herz algebras column and row operator spaces which we denote by col and row respectively over arbitrary banach spaces were introduced by the first named author for hilbert spaces these definitions coincide with the usual ones given a locally compact group g and p p 1 with 1p 1p 1 we use the operator space structure on cb col lp g to equip the figa talamanca herz algebra ap g with an operator space structure turning it into a quantized banach algebra moreover we show that for p q 2 or 2 q p and amenable g the canonical inclusion aq g ap g is completely bounded with cb norm at most kg2 where kg is grothendieck s constant as an application we show that g is amenable if and only if ap g is operator amenable for all and equivalently for one p 1 this extends a theorem by ruan

functional calculus for infinitesimal generators of holomorphic semigroups we give a functional calculus formula for infinitesimal generators of holomorphic semigroups of operators on banach spaces which involves the bochner riesz kernels of such generators the rate of smoothness of operating functions is related to the exponent of the growth on vertical lines of the operator norm of the semigroup the strength of the formula is tested on poisson and gauss semigroups inl1 rn andl1 g for a stratified lie groupg we give also a self contained theory of smooth absolutely continuous functions on the half line 0

measurable schur multipliers and completely bounded multipliers of the fourier algebras let g be a locally compact group and a g the fourier algebra of g from 17 in 24 herz de ned the space of herz schur multipliers b2 g he claimed that this space coincided with the space he denoted v g in his article 23 but o2ered no proof of this fact the completely bounded multipliers of the fourier algebra mcba g were de ned by de canniere and haagerup in 8 in was shown by bo zejko and fendler 7 that mcba g 1 4 b2 g isometrically unfortunately this result relies on unpublished work of gilbert entitled convolution operators and banach space tensor products i ii and iii but not widely available however there is a proof of the fact that mcba g 1 4 b2 g due to jolissaint 27 which relies on the representation theorem for completely bounded maps applied to the reduced c algebra c r g in this paper we prove an analogue of the fact that mcba g 1 4 b2 g in fact our result obtains that fact in the case that g is a discrete group and improves upon it in the respect that we obtain a complete isometry where both mcba g and b2 g are given natural operator space structures moreover we show that the natural module action of mcba g on the von neumann algebra generated by the left regular representation vn g extends completely isometrically to a normal action of mcba g on all of b l g the space of bounded operators on l g in fact the image of mcba g in the completely bounded normal maps on b l g consists of l1 g bimodule maps and can be characterised as a certain intrinsic invariant part amongst those maps we feel that our approach is interesting in and of itself since it makes systematic use of modern operator space theoretic techniques pioneered by blecher e2ros haagerup paulsen ruan and smith amongst others it thus gives a starting point for obtaining representations of completely bounded multipliers of kac algebras after 29 or of multipliers of locally compact quantum groups after vaes et al see 47 to support our approach in x 3 we describe the space of measurable schur multipliers v1 x for any suitable measure space x we develop the theory of v1 x fully and systematically our main tools for doing this are the results of smith 41 and blecher and smith 5 which characterise the normal completely bounded maps on the space of all bounded operators on a hilbert space which are module maps over a von neumann algebra we make great use of the weak haagerup tensor product of two von neumann algebras which is

one shot blind channel estimation for ofdm systems over frequency selective fading channels this paper presents a blind channel estimation bce technique for orthogonal frequency division multiplexing communications systems the proposed system is based on modulating particular pairs of subcarriers using amplitude shift keying and phase shift keying which enables the realization of a decision directed one shot bce osbce with complexity and accuracy that are comparable to pilot based channel estimation techniques the performance of the proposed estimator is evaluated in terms of the mean squared error mse where an accurate analytical expression is derived and verified using monte carlo simulation under various channel conditions the obtained results show that the mse of the proposed osbce is comparable to pilot based estimators which confirms the efficiency of the proposed osbce

spectral families of projections in hardy spaces strongly continuous one parameter groups of isometries in the reflexive hardy spaces of the disc d and the half plane are considered in the light of the author s previous joint result with h benzinger and t a gillespie which generalizes stone s theorem for unitary groups to arbitrary banach spaces it is shown that every such group tt of hardy space isometries has a spectral decomposition with respect to a suitable projection valued function on the real line r as in the classical statement of stone s theorem in hilbert space the relevant type of projection valued function is known as a spectral family this circle of ideas is intimately bound up with harmonic analysis particularly in hpr in particular if the group tt acts in hpd and is associated as in forelli s theorem with a group of parabolic mobius transformations of d then it can be analyzed by way of the translation group on hpr the stone type spectral family of the latter is shown to be obtained by restriction of the m riesz projections to hpr by this means a concrete description of the stone type spectral family for a parabolic isometric group on hpd is obtained a pleasant by product of the parabolic case is absorption of the classical paley wiener theorem for hpr 1 p 2 into the framework of the generalized stone s theorem

completely bounded homomorphisms of the fourier algebras abstract for locally compact groups g and h let a g denote the fourier algebra of g and b h the fourier stieltjes algebra of h any continuous piecewise affine map y h g where y is an element of the open coset ring induces a completely bounded homomorphism a g b h by setting u u on y and u 0 off of y we show that if g is amenable then any completely bounded homomorphism a g b h is of this form and this theorem fails if g contains a discrete nonabelian free group our result generalises results of cohen amer j math 82 1960 213 226 host bull soc math france 1986 114 and of the first author j funct anal 2004 213 we also obtain a description of all the idempotents in the fourier stieltjes algebras which are contractive or positive definite

conditional expectations on cv_ p g applications keywords locally compact groups amenable groups fourier algebra figa talamanca algebra convolution operators pseudomeasures reference cahru article 2007 001doi 10 1016 j jfa 2007 03 003view record in web of science record created on 2008 12 10 modified on 2016 08 08

steckin s theorem transference and spectral decompositions abstract let y be a closed subspace of lp where is an arbitrary measure and 1 sup v n n 0 1 2 in particular every surjective isometry of y can be expressed in the form v eia where a is well bounded of type b i e a has a spectral diagonalization analogous to though weaker than that in the spectral theorem for self adjoint operators this result which fails if y is replaced by an arbitrary reflexive space is obtained by a blend of the transference method of coifman and weiss with steckin s theorem and a recent result in abstract operator theory it has the direct consequence that every uniformly bounded one parameter group on y is the fourier stieltjes transform of a projection valued mapping of r an additional consequence is that every hermitian equivalent operator on y is well bounded of type b in the setting of an arbitrary banach space x power bounded operators with a logarithm of the form ia with a well bounded of type b are studied it is shown that if u is such an operator on x then for every function f of bounded variation on the unit circle n tf n u n converges in the strong operator topology this result which formally is a transference by u of steckin s theorem makes it possible to calculate directly from u a normalized logarithm for u and the spectral projections for the logarithm

stone s theorem for strongly continuous groups of isometries in hardy spaces for 1 p p 2 it is well known that a strongly continuous one parameter group of isometries in the hardy space hp d does not satisfy the classical stone theorem that is there is no additive spectral measure on the borel sets of the real line whose fourier stieltjes transform is the given group however if we relax the topology of hp d by imbedding it into some larger space then it is shown for the case of 1 p 2 that any such group does satisfy stone s theorem when considered as acting in some appropriate larger space the situation for 2 p is more complicated if the group of isometries is of elliptic type then it again satisfies stone s theorem in a suitable larger space however for parabolic groups the situation is fundamentally different such a group can never be interpreted as a fourier stieltjes transform in any space containing hp d

spectral decompositions of one parameter groups of isometries on hardy spaces spectral decompositions of strongly continuous one parameter groups of surjective isometries on hardy spaces of the disk d and the torus t2 are examined a concrete descriptiofi of the pointwise action of these decompositions is presented mainly in the parabolic case leading to a complete description of the action of the partial sum operators of m riesz when carried from lp r to hp d 1 p 2 the pointwise action of the spectral decompositions of these isometric groups on hp t2 1 p oo is also examined and concrete descriptions are derived mainly in the parabolic case

spectral multiplier theorems via h infty calculus and r bounds we prove spectral multiplier theorems for hormander classes mathcal h alpha p for 0 sectorial operators a on banach spaces assuming a bounded h infty sigma sigma calculus for some sigma in 0 pi and norm and certain r bounds on one of the following families of operators the semigroup e za on mathbb c the wave operators e isa for s in mathbb r the resolvent lambda a 1 on mathbb c backslash mathbb r the imaginary powers a it for t in mathbb r or the bochner riesz means 1 a u alpha for u 0 in contrast to the existing literature we neither assume that a operates on an l p scale nor that a is self adjoint on a hilbert space furthermore we replace generalized gaussian or poisson bounds and maximal estimates by the weaker notion of r bounds which allow for a unified approach to spectral multiplier theorems in a more general setting in this setting our results are close to being optimal moreover we can give a characterization of the r bounded mathcal h alpha 1 calculus in terms of r boundedness of bochner riesz means

bochner riesz profile of anharmonic oscillator l d2dx2 x we investigate spectral multipliers bochner riesz means and the convergence of eigenfunction expansion corresponding to the schrodinger operator with anharmonic potential l d2dx2 x we show that the bochner riesz profile of the operator l completely coincides with such profile of the harmonic oscillator h d2dx2 x2 it is especially surprising because the bochner riesz profile of the one dimensional standard laplace operator is known to be essentially different and the case of operators h and l resembles more the profile of multidimensional laplace operators another surprising element of the main obtained result is the fact that the proof is not based on restriction type estimates and instead an entirely new perspective has to be developed to obtain the critical exponent for bochner riesz means convergence

ber reduction of ofdm based broadband communication systems over multipath channels with impulsive noise this paper presents an efficient technique to jointly mitigate the severe bit error rate ber performance degradation caused by impulsive noise in and multipath fading in broadband transmission systems the proposed system is based on a low complexity interleaving process applied after the inverse fast fourier transform ifft in orthogonal frequency division multiplexing ofdm systems hence it is denoted as time domain interleaving tdi the proposed tdi introduces both time and frequency diversity which can be used to effectively combat impairments such as in and frequency selective fading in addition to its substantial ber reduction capability the tdi does not degrade the spectral efficiency and has low computational complexity in frequency selective fading channels the ber of the proposed system is mathematically equal to that of walsh hadamard precoded ofdm systems 1 in presence of in analytical and simulation results show that tdi can remarkably reduce the level of the error floors that are commonly observed specifically tdi can achieve a ber of 10 5 for less than 1 db difference from the in free case

amenable unitary representations of locally compact groups a notion of amenability for an arbitrary unitary group representation is introduced this unifies and generalizes the notions of amenable homogeneous spaces and of inner amenable groups amenable locally compact groups are characterized by the amenability of all their unitary representations amenable representations are characterized by several properties which are operator theoretic analogues of properties characterizing amenable groups we give a generalization to arbitrary representations of hulanicki reiter theorem this is used in order to describe the amenable representations of the groups with kazhdan property t

continuous sheffer families ii abstract continuous sheffer families have been recently introduced by the authors these are continuous versions of the sheffer sequences arising in the umbral calculus we show here that quite a number of classical special functions are examples of such families

joint data detection and channel estimation for ofdm systems we develop new blind and semi blind data detectors and channel estimators for orthogonal frequency division multiplexing ofdm systems our data detectors require minimizing a complex integer quadratic form in the data vector the semi blind detector uses both channel correlation and noise variance the quadratic for the blind detector suffers from rank deficiency for this we give a low complexity solution avoiding a computationally prohibitive exhaustive search we solve our data detectors using sphere decoding sd and v blast and provide simple adaptations of the sd algorithm we consider how the blind detector performs under mismatch generalize the basic data detectors to nonunitary constellations and extend them to systems with pilots and virtual carriers simulations show that our data detectors perform well

blind channel estimation for mimo ofdm systems via nonredundant linear precoding based on the assumption that the transmitted symbols are independent and identically distributed i i d we develop a simple subspace based blind channel estimation technique for orthogonal frequency division multiplexing ofdm systems by utilizing nonredundant linear block precoding a novel contribution is that the proposed method can be applied for scenarios where the number of receive antennas is less than the number of transmit antennas e g multiple input single output miso transmissions in which case the traditional subspace based methods could not be applied further consideration that can eliminate the multidimensional ambiguity in channel estimation under multiple transmitter scenarios is also proposed the numerical results clearly show the effectiveness of our proposed algorithm

bounds for spectral multipliers on nilpotent groups a criterion is given for the lp boundedness of a class of spec tral multiplier operators associated to left invariant homogeneous subelliptic second order differential operators on nilpotent lie groups generalizing a theo rem of hormander for radial fourier multipliers on euclidean space the order of differentiability required is half the homogeneous dimension of the group improving previous results in the same direction

low complexity blind equalization for ofdm systems with general constellations this paper proposes a low complexity algorithm for blind equalization of data in orthogonal frequency division multiplexing ofdm based wireless systems with general constellations the proposed algorithm is able to recover the transmitted data even when the channel changes on a symbol by symbol basis making it suitable for fast fading channels the proposed algorithm does not require any statistical information about the channel and thus does not suffer from latency normally associated with blind methods the paper demonstrates how to reduce the complexity of the algorithm which becomes especially low at high signal to noise ratio snr specifically it is shown that in the high snr regime the number of operations is of the order o ln where l is the cyclic prefix length and n is the total number of subcarriers simulation results confirm the favorable performance of the proposed algorithm

mapping ideals of quantum group multipliers abstract we study the dual relationship between quantum group convolution maps l 1 g l g and completely bounded multipliers of g for a large class of locally compact quantum groups g we completely isomorphically identify the mapping ideal of row hilbert space factorizable convolution maps with m c b l 1 g yielding a quantum gilbert representation for completely bounded multipliers we also identify the mapping ideals of completely integral and completely nuclear convolution maps the latter coinciding with l 1 b g where b g is the quantum bohr compactification of g for quantum groups whose dual has bounded degree we show that the completely compact convolution maps coincide with c b g our techniques comprise a mixture of operator space theory and abstract harmonic analysis including fubini tensor products the non commutative grothendieck inequality quantum eberlein compactifications and a suitable notion of inner co amenable quantum group that we introduce and for which we exhibit examples from the bicrossed product construction our main results are new even in the setting of group von neumann algebras v n g for quasi sin locally compact groups g

plancherel type estimates and sharp spectral multipliers abstract we study general spectral multiplier theorems for self adjoint positive definite operators on l2 x where x is any open subset of a space of homogeneous type we show that the sharp hormander type spectral multiplier theorems follow from the appropriate estimates of the l2 norm of the kernel of spectral multipliers and the gaussian bounds for the corresponding heat kernel the sharp hormander type spectral multiplier theorems are motivated and connected with sharp estimates for the critical exponent for the riesz means summability which we also study here we discuss several examples which include sharp spectral multiplier theorems for a class of scattering operators on r3 and new spectral multiplier theorems for the laguerre and hermite expansions

error probability analysis and applications of amplitude coherent detection in flat rayleigh fading channels this paper presents the detector design and symbol error rate ser analysis of m ary amplitude shift keying over multipath fading channels using amplitude coherent detection acd the optimum detector is derived using the maximum likelihood criterion and then it is used to derive two efficient low complexity suboptimal detectors the probability distribution function of the decision variables and the ser of the two suboptimal detectors are expressed using simple closed form analytical formulas when single receiving antenna is used the ser with receiver diversity is obtained using monte carlo simulation the obtained analytical and simulation results reveal that acd can provide reliable ser as compared with noncoherent detection moreover we present an efficient blind channel estimation algorithm using acd and hybrid modulation frame structures

spectral decompositions of hyperbolic isometric groups in hardy spaces of the disk abstract we introduce a mechanism that can be used to achieve concrete descriptions of the pointwise action of the spectral decompositions for the hyperbolic type groups of isometries on hp d 1

fourier multipliers in banach function spaces with umd concavifications we prove various extensions of the coifman rubio de francia semmes multiplier theorem to operator valued multipliers on banach function spaces our results involve a new boundedness condition on sets of operators which we call ell r ell s boundedness which implies mathcal r boundedness in many cases the proofs are based on new littlewood paley rubio de francia type estimates in banach function spaces which were recently obtained by the authors