multi parameter automodels and their applications summary motivated by the modelling of non gaussian data or positively correlated data on a lattice extensions of besag s automodels to exponential families with multi dimensional parameters have been proposed recently we provide a multiple parameter analogue of besag s one dimensional result that gives the necessary form of the exponential families for the markov random field s conditional distributions we propose estimation of parameters by maximum pseudolikelihood and give a proof of the consistency of the estimators for the multi parameter automodel the methodology is illustrated with examples in particular the building of a cooperative system with beta conditional distributions we also indicate future applications of these models to the analysis of mixed state spatial data

on the poisson transform on symmetric spaces of real rank one abstract in this paper we investigate l 2 boundedness properties of the poisson transform associated to a symmetric space of real rank one and prove a related plancherel type theorem

harmonic analysis as spectral theory of laplacians by writing the fourier inversion formula on euclidean space in polar coordinates we obtain f x 0 fgl x dx where fgl x 2fgl x which is the spectral theory of the laplacian how do properties of f relate to properties of the family of eigenfunctions fgl answers are provided for the following spaces l2 s s d in odd dimensions analogous results are obtained for harmonic analysis on hyperbolic space constant curvature semi riemannian spaces the heisenberg group and for differential forms on hyperbolic space for f l2 there is a plancherel formula f 22 limt o 1t bt z f x 2dx d where bt z denotes the ball of radius t about an arbitrary point z which is independent of the dimension and the identical formula holds in hyperbolic space if the parametrization of the eigenvalues is shifted for certain semi riemannian symmetric spaces we obtain a paley wiener theorem that explains the role of discrete series in producing functions of compact support and also involve certain non unitary representations that contain the discrete series representations for the heisenberg group the plancherel formula is of a different nature requiring that the eigenfunctions be almost periodic in one variable

asymptotic expansions and boundary values of eigenfunctions on riemannian symmetric spaces soit x g k un espace de riemann symetrique de type non compacte a bord b k m et soit d x l algebre de tous les operateurs differentiels g invariants sur x on obtient des developpements asymptotiques pour une grande classe de fonctions jointives f sur x

partially coupled stochastic gradient identification methods for non uniformly sampled systems this technical note addresses identification problems of non uniformly sampled systems for the input output representation of non uniform discrete time systems a partially coupled stochastic gradient c sg algorithm is proposed to estimate the model parameters with high computational efficiency compared with the standard stochastic gradient sg algorithm the analysis indicates that the partially c sg algorithm can give more accurate parameter estimates than the sg algorithm the parameter estimates obtained using the partially c sg algorithm converge to their true values as the data length approaches infinity

dispersive estimates for the dirac equation in an aharonov bohm field abstract we prove local smoothing and weighted strichartz estimates for the dirac equation with a aharonov bohm potential the proof inspired by 12 relies on an explicit representation of the solution built in terms of spectral projections

performance analysis of multi innovation gradient type identification methods it is well known that the stochastic gradient sg identification algorithm has poor convergence rate in order to improve the convergence rate we extend the sg algorithm from the viewpoint of innovation modification and present multi innovation gradient type identification algorithms including a multi innovation stochastic gradient misg algorithm and a multi innovation forgetting gradient mifg algorithm because the multi innovation gradient type algorithms use not only the current data but also the past data at each iteration parameter estimation accuracy can be improved finally the performance analysis and simulation results show that the proposed misg and mifg algorithms have faster convergence rates and better tracking performance than their corresponding sg algorithms

characterization of eigenfunctions of the laplacian by boundedness conditions if f k x k z is a doubly infinite sequence of functions on r n which are uniformly bounded and such that f k f k 1 then f 0 f 0 this generalizes a therem of roe n 1 the analogous statement is true on the heisenberg group but false in hyperbolic space

pointwise fourier inversion on rank one symmetric spaces and related topics abstract this paper develops necessary and sufficient conditions for pointwise inversion of fourier transforms on rank one symmetric spaces of non compact type for functions in the piecewise smooth category this extends results of pinsky for isotropic riemannian manifolds of constant curvature methodologically a similar result on the jacobi transform and a transplantation scheme from even dimensional spaces to certain odd dimensional real hyperbolic spaces naturally enter the picture

transformations between some special matrices special matrices are very useful in signal processing and control systems this paper studies the transformations and relationships between some special matrices the conditions that a matrix is similar to a companion matrix are derived it is proved that a companion matrix is similar to a diagonal matrix or jordan matrix and the transformation matrices between them are given finally we apply the similarity transformation and the companion matrix to system identification

lp contractive projections and the heat semigroup for differential forms a projection operator that is contractive on lp for two distinct values of p is shown to be contractive for all values of p and the range must be of a special form this result is used to show that the heat semigroup for k forms on many manifolds with nontrivial cohomology in dimension k cannot be contractive on any lp for p 2

computation of matrix exponentials of special matrices computing matrix exponentials or transition matrices are important in signal processing and control systems this paper studies the methods of computing the transition matrices related to linear dynamic systems discusses and gives the properties of the transition matrices and explores the transition matrices of some special matrices some examples are provided to illustrate the proposed methods

fourier asymptotics of fractal measures abstract a measure on r n will be called locally uniformly dimensional if br x cr for all r 1 and all x where br x denotes the ball of radius r about x for l 2 d the measure d is in i so d is well defined we show it is locally in l2 and sup r 1 r n b r y f d 2 d c f 2 under additional hypotheses we show that lim r r n b r y f d 2 2 d is comparable in size to 2 2 a number of other related results are established the special case when is an integer and is the surface measure on a c1 manifold was treated by s agmon and l hormander j analyse math 30 1976 1 38

iterative solutions of the generalized sylvester matrix equations by using the hierarchical identification principle abstract in this paper by extending the well known jacobi and gauss seidel iterations for ax b we study iterative solutions of matrix equations axb f and generalized sylvester matrix equations axb cxd f including the sylvester equation ax xb f as a special case and present a gradient based and a least squares based iterative algorithms for the solution it is proved that the iterative solution always converges to the exact solution for any initial values the basic idea is to regard the unknown matrix x to be solved as the parameters of a system to be identified and to obtain the iterative solutions by applying the hierarchical identification principle finally we test the algorithms and show their effectiveness using a numerical example

output feedback stabilization of networked control systems with random delays modeled by markov chains this note investigates the output feedback stabilization of networked control systems ncss the sensor to controller s c and controller to actuator c a random network induced delays are modeled as markov chains the focus is on the design of a two mode dependent controller that depends on not only the current s c delay but also the most recent available c a delay at the controller node the resulting closed loop system is transformed to a special discrete time jump linear system then the sufficient and necessary conditions for the stochastic stability are established further the output feedback controller is designed via the iterative linear matrix inequality lmi approach simulation examples illustrate the effectiveness of the proposed method

random fields on a network modeling statistics and applications the theory of spatial models over lattices or random fields as they are known has developed significantly over recent years this book provides a graduate level introduction to the subject which assumes only a basic knowledge of probability and statistics finite markov chains and the spectral theory of second order processes a particular strength of this book is its emphasis on examples both to motivate the theory which is being developed and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms

kalman state filtering based least squares iterative parameter estimation for observer canonical state space systems using decomposition this paper focuses on the parameter and state estimation problems for observer canonical state space systems from measurement information derives a kalman filter based least squares iterative kf lsi algorithm to estimate the parameters and states and a model decomposition based kf lsi algorithm to enhance computational efficiency an example is provided to confirm the effectiveness of the proposed algorithms

on iterative solutions of general coupled matrix equations in this paper we study coupled matrix equations which are encountered in many systems and control applications first we extend the well known jacobi and gauss seidel iterations and present a large family of iterative methods which are then applied to develop iterative solutions to coupled sylvester matrix equations the basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified and to obtain the iterative solutions by applying a hierarchical identification principle next we generalize the sylvester equations to general coupled matrix equations and propose a gradient based iterative algorithm for the solutions using a block matrix inner product the star star product we prove that the iterative algorithm always converges to the unique solutions for any initial values one advantage of the algorithms proposed is that they require less storage space in implementation than existing numerical methods finally we test the algorithms and show their effectiveness using numerical examples

the residual based interactive stochastic gradient algorithms for controlled moving average models this paper derives a residual based interactive stochastic gradient isg parameter estimation algorithm for controlled moving average cma models and studied the performance of the residual based isg algorithm under weaker conditions on statistical properties of the noise compared with the residual based extended stochastic gradient algorithm for identifying cma models the proposed isg algorithm can give highly accurate parameter estimates by the simulation example

explicit solutions of maxwell s equations on a space of constant curvature abstract an explicit solution is given to the cauchy problem for the source free maxwell s equations in a vacuum on a space time of the form r 1 x m3 where m3 is a 3 manifold of constant curvature this solution satisfies huyghens principle that all electromagnetic radiation propagates at exactly the speed of light the solution is obtained by harmonic analysis on m3 and in the process a generating class of plane wave solutions is found these solutions approximate the flat space plane wave solutions in a neighbourhood of a point but their global properties are somewhat different the solutions obtained are easily transplanted to the robertson walker models of general relativity by re scaling the time variable

uncertainty principles in harmonic analysis abstract let l 2 r n 2 1 generalizing the heisenberg uncertainty principle lower bounds for the variance of the measure x 2 dx are established under assumptions on the fourier transform tf if e is a subset of r n of codimension one which is suitably uniformly distributed and b is a parameter which measures the maximum distance from a point to e then the estimate var x 2 dx cb 2 holds provided e tf 2 d c b 1 for suitable constants c and c examples of sets e are families of parallel hyperspaces or concentric spheres analogous results are established for normalized l 2 functions on the sphere s n here the lower bound is inf y s n s n sin d x y 2 x 2 dx cb 2 and the hypothesis on the spherical harmonic expansion k 0 k is k a k 2 2 c b 1 where a is a set of integers with gaps at most b for both even and odd numbers

local ergodic theorems for k spherical averages on the heisenberg group given a gelfand pair h n k where h n is the heisenberg group and k is a compact subgroup of the unitary group u n we consider the sphere and ball averages of certain k invariant measures on h n we prove local ergodic theorems for these measures when n geq 3 we also consider averages over annuli in the case of reduced heisenberg group and show that when the functions have zero mean value the maximal function associated to the annulus averages behave better than the spherical maximal function we use square function arguments which require several properties of the k spherical functions

estimates for sums of eigenvalues for domains in homogeneous spaces abstract let 0hgr mbe a bounded open subset of a homogeneous riemannian manifold and let k 1 kbe the sum of the firstkeigenvalues of the dirichlet laplacian on 0hgr and similarly k 1 kfor the neumann laplacian we give bounds for kand kgeneralizing results of li yau and kroger in the casem r n we prove a generic theorem which in the case of compactmsays k p 0hgr k p 0hgr kwherep 0hgr 0hgr m is the relative volume of 0hgr and x is the eigenvalue sum function form interpolated linearly for non integer values for noncompactmthe statement is k 0hgr k 0hgr where is a renormalized eigenvalue sum function form defined using the spectral resolution of onm there are also estimates in the other direction of the same form with error terms the same generic theorems hold for laplacian onp forms and for subelliptic laplacians on subriemannian manifolds to give life to such generic theorems it is necessary to compute the function for a variety of examples for euclideann space x n n 2 cnx1 2 nwherecnis the weyl constant so our generic result includes the known results we discuss the computation of for spheres hyperbolic spaces noncompact symmetric spaces and the heisenberg groups

simultaneous motion detection and background reconstruction with a conditional mixed state markov random field in this work we present a new way of simultaneously solving the problems of motion detection and background image reconstruction an accurate estimation of the background is only possible if we locate the moving objects meanwhile a correct motion detection is achieved if we have a good available background model the key of our joint approach is to define a single random process that can take two types of values instead of defining two different processes one symbolic motion detection and one numeric background intensity estimation it thus allows to exploit the spatio temporal interaction between a decision motion detection and an estimation intensity reconstruction problem consequently the meaning of solving both tasks jointly is to obtain a single optimal estimate of such a process the intrinsic interaction and simultaneity between both problems is shown to be better modeled within the so called mixed state statistical framework which is extended here to account for symbolic states and conditional random fields experiments on real sequences and comparisons with existing motion detection methods support our proposal further implications for video sequence inpainting will be also discussed

hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems according to the hierarchical identification principle a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems i e multivariable oema like models which is different from multivariable carma like models as there exist unmeasurable noise free outputs and unknown noise terms in the information vector matrix of the corresponding identification model this paper is by means of the auxiliary model identification idea to replace the unmeasurable variables in the information vector matrix with the estimated residuals and the outputs of the auxiliary model a numerical example is provided

the campbell baker hausdorff dynkin formula and solutions of differential equations the campbell baker hausdorff dynkin formula is a special case of a simpler and more general formula for the solution of nonautonomous systems of first order ordinary differential equations in terms of autonomous systems specifically suppose u t takes values in a c manifold and satisfies the initial value problem u t a t u t u 0 a where a t is a vector field on the manifold depending continuously on t then u t exp z t a here exp z a means the solution at s 1 to v s z v s v 0 a for z t r 1 pr e r2r 1e tr t x a s 1 a s 2 a s r ds as t 0 where tr t s rr 0 s1 s2 sr t pr is the set of permutations on 1 r e is the number of errors in ordering consecutive terms in 1 r and is the usual commutator of vector fields under appropriate analyticity assumptions the series for z t is convergent for small t this formula gives an explicit formulation of results of k t chen published in 1957 applications are given to problems in sub riemannian geometry and to improving convergence estimates for the campbell baker hausdorff dynkin formula in the context of banach algebras our formula can be thought of as a noncommutative generalization of the familiar formula u t a exp 0t a s ds in the scalar linear case in the same way that the campbell baker hausdorff dynkin formula is a noncommutative generalization of the familiar formula exey ex y

image of the schwartz space under spectral projection let x g k be a riemannian symmetric space of non compact type and rank one the spectral projection p f of a function f on x can be written p f f where is the elementary spherical function corresponding to the complex parameter we characterize the image of the schwartz space mathcal s p x under the spectral projection for 0 p 2

maximum likelihood stochastic gradient estimation for hammerstein systems with colored noise based on the key term separation technique this paper considers the identification problems of hammerstein finite impulse response moving average fir ma systems using the maximum likelihood principle and stochastic gradient method based on the key term separation technique in order to improve the convergence rate a maximum likelihood multi innovation stochastic gradient algorithm is presented the simulation results show that the proposed algorithms can effectively estimate the parameters of the hammerstein fir ma systems

multi innovation stochastic gradient algorithm for multiple input single output systems using the auxiliary model in order to reduce computational burden and improve the convergence rate of identification algorithms an auxiliary model based multi innovation stochastic gradient am misg algorithm is derived for the multiple input single output systems by means of the auxiliary model identification idea and multi innovation identification theory the basic idea is to replace the unknown outputs of the fictitious subsystems in the information vector with the outputs of the auxiliary models and to present an auxiliary model based stochastic gradient algorithm and then to derive the am misg algorithm by expanding the scalar innovation to innovation vector and introducing the innovation length the simulation example shows that the proposed algorithms work quite well

a proportional differential control method for a time delay system using the taylor expansion approximation abstract in this paper a proportional differential control algorithm is studied according to the system performance indices we uses the first order taylor expansion to approximate the time delay present an algorithm to determine the controller parameters so that the desired dynamic performance can be achieved the numerical examples are provided to show the advantages of the proposed algorithm for small time delay

lp harmonic analysis and radon transforms on the heisenberg group in this paper harmonic analysis in the heisenberg group heisn cn r with group law z t z t z z t t 12im z z is taken to mean the joint spectral theory of the operators l heisenberg laplacian and t t the spectral decomposition of e l2 is given explicitly as e 0 e d where e 1 k 0 1 2 and e z t n 2 n 1 n 2k n 1 exp ie tn 2k exp z 24 n 2k lkn 1 z 22 n 2k where lkn 1 denotes the laguerre polynomial the eigenvalues are it e e n 2k e and l k e k e this decomposition is essentially well known but has not previously been described in this light it is also the decomposition into irreducibles of the representation of the heisenberg motion group semi direct product of heisn and u n on l2 heisn the main result is a summability in lp of the decomposition for e lp 1 p limr 1 rk 0 ed for p 1 only a weaker substitute is available and for p the decomposition is false there is also a plancherel formula for l2 2 2 k e n 2k 0 k e z 0 2dzd a number of explicit examples of the decomposition are computed including part of the schrodinger propagator eisl the heisenberg radon transform is defined by r z t n z t w 0 dw this operator was studied by geller and stein it is shown to be bounded from lp to lq if and only if p 2n 2 2n 1 and q 2n 2 some generalizations of these results to the free step two nilpotent lie groups are given but the results are not as complete

characterization of eigenfunctions of the laplace beltrami operator using fourier multipliers abstract let x be a rank one riemannian symmetric space of noncompact type and be the laplace beltrami operator of x the space x can be identified with the quotient space g k where g is a connected noncompact semisimple lie group of real rank one with finite center and k is a maximal compact subgroup of g thus g acts naturally on x by left translations through this identification a function or measure on x is radial i e depends only on the distance from ek when it is invariant under the left action of k we consider right convolution operators on functions f on x defined by f f where is a radial possibly complex measure on x these operators will be called multipliers in particular is a radial average when is a radial probability measure notable examples of radial averages are ball sphere and annular averages and the heat operator in this paper we address problems of the following type fix a multiplier in particular an averaging operator suppose that f k k z is a bi infinite sequence of functions on x such that for all k z f k a f k 1 and f k m for some constants a c m 0 and a suitable norm from this hypothesis we try to infer that f 0 hence every f k is an eigenfunction of

on the power method for quaternion right eigenvalue problem abstract in this paper we study the power method of the right eigenvalue problem of a quaternion matrix a if a is hermitian we propose the power method that is a direct generalization of that of complex hermitian matrix when a is non hermitian by applying the properties of quaternion right eigenvalues we propose the power method for computing the standard right eigenvalue with the maximum norm and the associated eigenvector we also briefly discuss the inverse power method and shift inverse power method for the both cases the real structure preserving algorithm of the power method in the two cases are also proposed and numerical examples are provided to illustrate the efficiency of the proposed power method and inverse power method

solutions to a family of matrix equations by using the kronecker matrix polynomials closed form solutions to a family of generalized sylvester matrix equation in form of i 0 fa ixf email protected i 0 jb kyf email protected j 0 fe jrf j are given by using the so called kronecker matrix polynomials it is found that the structure of the solutions is independent of the orders f j and f this type of uniform closed form solutions includes our early results as special cases the results provide great convenience to the computation and analysis of the solutions to this class of equations and can perform important functions in many analysis and design problems in linear systems

local harmonic analysis on spheres abstract a continuous expansion x x h d is established for functions or distributions supported on a sufficiently small set k in the sphere sn valid in a neighborhood of k where x are eigenfunctions of the laplacian on with eigenvalue n 1 2 2 2 the function h and the operators p that give from are given by explicit formulas when n is odd the function x can be uniquely characterized by analyticity and growth conditions in of paley wiener type the expansion is applied to study functions of the laplacian and operators that commute with the laplacian

mean value properties of the laplacian via spectral theory soit z 2 une fonction entiere paire de type exponentiel temperee l une realisation auto adjointe de c x ou est l operateur de laplace beltrami sur une variete de riemann et l l operateur donne par la theorie spectrale on demontre un theoreme de paley wiener sur le support de l et on l utilise pour montrer que lu u sur un bon domaine implique l u u

the spherical transform of a schwartz function on the heisenberg group suppose thatk u n is a compact lie group acting on the 2n 1 dimensional heisenberg grouphn we say that k hn is a gelfand pair if the convolution algebral1k hn of integrablek invariant functions onhnis commutative in this case the gelfand space k hn is equipped with the godement plancherel measure and the spherical transform l2k hn l2 k hn is an isometry the main result in this paper provides a complete characterization of the set sk hn f f sk hn of spherical transforms ofk invariant schwartz functions onhn we show that a functionfon k hn belongs to sk hn if and only if the functions obtained fromfvia application of certain derivatives and difference operators satisfy decay conditions we also consider spherical series expansions fork invariant schwartz functions onhnmodulo its center

iterative least squares solutions of coupled sylvester matrix equations abstract in this paper we present a general family of iterative methods to solve linear equations which includes the well known jacobi and gauss seidel iterations as its special cases the methods are extended to solve coupled sylvester matrix equations in our approach we regard the unknown matrices to be solved as the system parameters to be identified and propose a least squares iterative algorithm by applying a hierarchical identification principle and by introducing the block matrix inner product the star product for short we prove that the iterative solution consistently converges to the exact solution for any initial value the algorithms proposed require less storage capacity than the existing numerical ones finally the algorithms are tested on computer and the results verify the theoretical findings

self tuning control based on multi innovation stochastic gradient parameter estimation abstract this paper uses the multi innovation stochastic gradient misg algorithm to estimate the parameters of discrete time systems and presents an misg based self tuning control scheme furthermore we prove that the parameter estimation error converges to zero under persistent excitation and the parameter estimation based control algorithm can asymptotically achieve virtually optimal control and ensure that the closed loop systems are stable and globally convergent the simulation example is included

fourier restriction theorem and characterization of weak l2 eigenfunctions of the laplace beltrami operator abstract in this paper we prove that for r 0 the poisson transform p f of f l 2 k m belongs to l 2 g k this complements an earlier result of lohoue and rychener using this we then prove an analogue of tomas stein restriction theorem for riemannian symmetric spaces of noncompact type with real rank one by using this estimate of the poisson transform we also characterize all weak l 2 eigenfunction of the laplace beltrami operator of riemannian symmetric spaces of noncompact type with real rank one and eigenvalue 2 2 for r 0

l2 concrete spectral analysis of the invariant laplacianδαβin the unit complex ballbn for every fixed real number related to the continuous spectrum of the invariant laplacians 4 1 z 2 i j 1n ij zizj 2 zj zj j 1nzj zj j 1nzj zj inbn we characterize the eigenfunctions of that are poisson integrals ofl2 functions on the boundary ofbn these eigenfunctions occurred in the weighted plancherel formula of the unit complex ball see zhang studia math 102 2 1992 for the weighted plancherel formula in the ball the obtained characterization generalizes our announced result in boussejra and intissar c r acad sci 315 1992 1353 1357 for the bergman laplacian 00of the unit complex ball to the laplacians for arbitrary inr

some new connections between matrix products for partitioned and non partitioned matrices this paper is concerned with a long list of matrix products for partitioned and non partitioned matrices including kronecker khatri rao of first kind hadamard tracy singh khatri rao block kronecker block hadamard and box products sums our contribution is to gather the most useful connections of the matrix products from various sources and present them in one place several new attractive connections are also added to this collection we give as an example two applications in order to show that these connections play a central role in many applications these applications are a block diagonal least squares problem and a generalization of matrix inequalities involving khatri rao products of positive definite matrices

hierarchical least squares identification for linear siso systems with dual rate sampled data this technical note studies identification problems for dual rate sampled data linear systems with noises a hierarchical least squares hls identification algorithm is presented to estimate the parameters of the dual rate armax models the basic idea is to decompose the identification model of a dual rate system into several sub identification models with smaller dimensions and fewer parameters the proposed algorithm is more computationally efficient than the recursive least squares rls algorithm since the rls algorithm requires computing the covariance matrix of large sizes while the hls algorithm deals with the covariance matrix of small sizes compared with our previous work a detailed study of the hls algorithm is conducted in this technical note the performance analysis and simulation results confirm that the estimation accuracy of the proposed algorithm are close to that of the rls algorithm but the proposed algorithm retains much less computational burden

scattering theory for the laplacian on symmetric spaces of noncompact type and its application to a conjecture of strichartz abstract in this paper we develop the scattering theory for the laplacian on symmetric spaces of noncompact type we study the asymptotic properties of the resolvent in the framework of the agmon hormander space our approach is based on a detailed analysis of the helgason fourier transform and generalized spherical functions on symmetric spaces of noncompact type as an application of our scattering theory we prove a conjecture by strichartz concerning a characterization of a family of generalized eigenfunctions of the laplacian

orthogonal polynomial expansions for the matrix exponential many different algorithms have been suggested for computing the matrix exponential in this paper we put forward the idea of expanding in either chebyshev legendre or laguerre orthogonal polynomials in order for these expansions to converge quickly we cluster the eigenvalues into diagonal blocks and accelerate using shifting and scaling

convergence of stochastic gradient estimation algorithm for multivariable arx like systems this paper studies the convergence of the stochastic gradient identification algorithm of multi input multi output arx like systems i e multivariable arx like systems by using the stochastic martingale theory this arx like model contains a characteristic polynomial and differs from the conventional multivariable arx system the results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions the simulation results validate the proposed convergence theorem

harmonic analysis on constant curvature surfaces with point singularities let rn2 denote the n fold covering space of the plane with the origin deleted 0 n parametrized by polar coordinates r with periodic of period 2 n and equipped with the flat riemannian metric dr2 r2 d 2 there is a natural harmonic analysis with the fourier transform given by f c 12 0 f r j v r eiv r dr d fourier inversion formula f c 0 f r j v r eiv d dv and plancherel formula f 22 2 0 f v 2 d dv in the case n and analogous expressions with v restricted to the values kn when n is finite this harmonic analysis realizes the joint spectral decompositions of the self adjoint operators i and where is the dirichlet or friedrichs extension of the laplace beltrami operator defined on d this paper gives a detailed development of this harmonic analysis including the effect of basic differentiation and multiplication operators on the fourier transform the theory of l2 sobolev spaces hk and the distinctions between h2 the domain of and the space of functions f with both f and f in l2 in the process it is necessary to study certain generalizations of the hilbert transform that are related to the theory of hankel transforms two applications of this harmonic analysis are given to the study of a natural radon transform or x ray transform on rn2 and to the solution of the heat equation on rn2 the latter also gives information about the heat equation in a sector of the plane with dirichlet or neumann boundary conditions and about brownian motion in the plane taking into account the winding number of a brownian path with respect to the origin analogous problems for spaces of non zero constant curvature are discussed and in this context some higher dimensional spaces arise naturally

expansion in generalized eigenfunctions for laplacians on graphs and metric measure spaces we consider an arbitrary selfadjoint operator on a separable hilbert space to this operator we construct an expansion in generalized eigenfunctions in which the original hilbert space is decomposed as a direct integral of hilbert spaces consisting of general eigenfunctions this automatically gives a plancherel type formula for suitable operators on metric measure spaces we discuss some growth restrictions on the generalized eigenfunctions for laplacians on locally finite graphs the generalized eigenfunctions are exactly the solutions of the cor responding difference equation

a characterization of the l2 range of the poisson transform related to strichartz conjecture on symmetric spaces of noncompact type abstract the main purpose of this paper is to solve strichartz conjecture concerning an image characterization of the poisson transform in the l 2 theory on symmetric spaces of noncompact type we prove that the poisson transform provides an isomorphism between the l 2 space on the boundary and a certain weighted l 2 space consisting of joint eigenfunctions on symmetric spaces of noncompact type our approach is based on the scattering theory for the schrodinger operator moreover we give a fourier restriction estimate and an asymptotic formula for the poisson transform

eigenspaces of the laplacian on hyperbolic spaces composition series and integral transforms abstract let x be a projective real complex or quaternion hyperbolic space realized as the pseudo riemannian symmetric space x g h with g o p q u p q or sp p q these are the classical isotropic symmetric spaces let be the g invariant laplace beltrami operator on x a complete description by k types for each c of all closed g invariant subspaces of the eigenspace f c x f f is given the eigenspace representations are compared with principal series representations using poisson transformations similar results are obtained also for the exceptional isotropic symmetric space the langlands parameters of the spherical discrete series representations are determined