a non hyponormal operator generating stieltjes moment sequences abstract a linear operator s in a complex hilbert space h for which the set d s of its c vectors is dense in h and s n f 2 n 0 is a stieltjes moment sequence for every f d s is said to generate stieltjes moment sequences it is shown that there exists a closed non hyponormal operator s which generates stieltjes moment sequences what is more d s is a core of any power s n of s this is established with the help of a weighted shift on a directed tree with one branching vertex the main tool in the construction comes from the theory of indeterminate stieltjes moment sequences as a consequence it is shown that there exists a non hyponormal composition operator in an l 2 space over a finite measure space which is injective paranormal and which generates stieltjes moment sequences the independence assertion of barry simon s theorem which parameterizes von neumann extensions of a closed real symmetric operator with deficiency indices 1 1 is shown to be false

unbounded subnormal weighted shifts on directed trees ii abstract a new method of verifying the subnormality of unbounded hilbert space operators based on an approximation technique is proposed diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established an approach to this issue via consistent systems of probability measures is invented the role played by determinate stieltjes moment sequences is elucidated lambert s characterization of subnormality of bounded operators is shown to be valid for unbounded weighted shifts on directed trees that have sufficiently many quasi analytic vectors which is a new phenomenon in this area

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

essential self adjointness of the graph laplacian we study the operator theory associated with such infinite graphs g as occur in electrical networks in fractals in statistical mechanics and even in internet search engines our emphasis is on the determination of spectral data for a natural laplace operator associated with the graph in question this operator will depend not only on g but also on a prescribed positive real valued function c defined on the edges in g in electrical network models this function c will determine a conductance number for each edge we show that the corresponding laplace operator is automatically essential self adjoint by this we mean that is defined on the dense subspace d of all the real valued functions on the set of vertices g0 with finite support in the hilbert space l2 g0 the conclusion is that the closure of the operator is self adjoint in l2 g0 and so in particular that it has a unique spectral resolution determined by a projection valued measure on the borel subsets of the infinite half line we

reduced commutativity of moduli of operators abstract in this paper we investigate the question of when the equations a s a s a a s s s where s is a finite set of positive integers imply the quasinormality or normality of a in particular it is proved that if s p m m p n n p where p 1 and 2 m n then a is quasinormal moreover if a is invertible and s m n n m with m n then a is normal the case when s m m n and a n a n a a n is also discussed

unified probability density function involving a confluent hypergeometric function of two variables in this paper first we define a new gamma type function by means of an integral involving the confluent hypergeometric function of two variables f 1 a b c w z the gamma type function is expressed in explicit form using generalized hypergeometric series associated incomplete functions are defined some special cases are noted and some relations for the new gamma type function are given a generalized probability density is considered using the gamma type function this density represents a unified form for several gamma type and inverse gaussian densities a new probability density function with gauss hypergeometric function is obtained a number of known probability density functions follow as special cases some statistical functions associated with the new density are obtained some figures are drawn for the probability density to show the effect of the parameters involved results given recently by al zamel ali et al and others can be recovered from the formulas established here

subnormality of unbounded composition operators over one circuit directed graphs exotic examples abstract a recent example of a non hyponormal injective composition operator in an l 2 space generating stieltjes moment sequences invented by three of the present authors was built over a non locally finite directed tree the main goal of this paper is to solve the problem of whether there exists such an operator over a locally finite directed graph and in the affirmative case to find the simplest possible graph with these properties simplicity refers to local valency the problem is solved affirmatively for the locally finite directed graph g 2 0 which consists of two branches and one loop the only simpler directed graph for which the problem remains unsolved consists of one branch and one loop the consistency condition the only efficient tool for verifying subnormality of unbounded composition operators is intensively studied in the context of g 2 0 which leads to a constructive method of solving the problem the method itself is partly based on transforming the krein and the friedrichs measures coming either from shifted al salam carlitz q polynomials or from a quartic birth and death process

quasinormal extensions of subnormal operator weighted composition operators in l2 spaces abstract we prove the subnormality of an operator weighted composition operator whose symbol is a transformation of a discrete measure space and whose weights are multiplication operators in l 2 spaces under the assumption of existence of a family of probability measures whose radon nikodym derivatives behave regular along the trajectories of the symbol we build the quasinormal extension which is a weighted composition operator induced by the same symbol we give auxiliary results concerning commutativity of operator weighted composition operators with multiplication operators

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

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

unbounded subnormal composition operators in l2 spaces abstract a novel criterion for subnormality of unbounded composition operators in l 2 spaces written in terms of measurable families of probability measures satisfying the so called consistency condition is established it becomes a new characterization of subnormality in the case of bounded composition operators pseudo moments of a measurable family of probability measures that satisfies the consistency condition are proved to be given by the radon nikodym derivatives which appear in lambert s characterization of bounded composition operators a criterion for subnormality of composition operators induced by matrices is provided the question of subnormality of composition operators over discrete measure spaces is studied two new classes of subnormal composition operators over discrete measure spaces are introduced a recent criterion for subnormality of weighted shifts on directed trees by the present authors is essentially improved in the case of rootless directed trees and nonzero weights by dropping the assumption of density of c vectors in the underlying l 2 space

a unified form of gamma type distributions we study a mathematical model for a new distribution involving the generalized gamma function of al musallam and kalla further results on a generalized gamma function occurring in diffraction theory integral transform spec funct 7 1998 175 190 the probability density function p d f is defined and some special cases are noted we derive some basic functions associated with the p d f namely the mean moment generating function hazard rate function and mean residue life function comparative graphs of p d f hazard rate function and mean residue life function are given these graphs are found to reflect the role of shape and scale parameters

unbounded extensions and operator moment problems abstract extension results expressed in terms of complete boundedness leading to necessary and sufficient conditions for the solvability of power moment problems with unbounded operator data are given as an application necessary and sufficient conditions for the existence of selfadjoint and normal extensions for some classes of commuting tuples of unbounded linear operators are obtained

commuting self adjoint extensions of symmetric operators defined from the partial derivatives we consider the problem of finding commuting self adjoint extensions of the partial derivatives 1 i xj j 1 d with domain cc where the self adjointness is defined relative to l2 and is a given open subset of rd the measure on is lebesgue measure on rd restricted to the problem originates with segal and fuglede and is difficult in general in this paper we provide a representation theoretic answer in the special case when i 2 and i is an open interval we then apply the results to the case when is a d cube id and we describe possible subsets rd such that e id is an orthonormal basis in l2 id

a solution to the cauchy dual subnormality problem for 2 isometries abstract the cauchy dual subnormality problem asks whether the cauchy dual operator t t t t 1 of a 2 isometry t is subnormal in the present paper we show that the problem has a negative solution the first counterexample depends heavily on a reconstruction theorem stating that if t is a 2 isometric weighted shift on a rooted directed tree with nonzero weights that satisfies the perturbed kernel condition then t is subnormal if and only if t satisfies the unperturbed kernel condition the second counterexample arises from a 2 isometric adjacency operator of a locally finite rooted directed tree again by thorough investigations of positive solutions of the cauchy dual subnormality problem in this context we prove that if t is a 2 isometry satisfying the kernel condition or a quasi brownian isometry then t is subnormal we construct a 2 isometric adjacency operator t of a rooted directed tree such that t does not satisfy the kernel condition t is not a quasi brownian isometry and t is subnormal

on the ϰth root of a stieltjes moment sequence abstract stieltjes moment sequences a n n 0 whose th roots a n n 0 are stieltjes moment sequences are studied is a fixed integer greater than or equal to 2 a formula connecting the closed supports of representing measures of a n n 0 and a n n 0 is established the relationship between the holes of the supports of these measures is investigated the set of all pairs m n of positive integers for which there exists a stieltjes moment sequence whose square root is a stieltjes moment sequence and both of them have representing measures supported on subsets of 0 of cardinality m and n respectively is described

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

fields over unsharp coordinates it has been shown that space time coordinates can exhibit only very few types of short distance structures if described by linear operators they can be continuous discrete or unsharp in one of two ways in the literature various quantum gravity models of space time at short distances point towards one of these two types of unsharpness here we investigate the properties of fields over such unsharp coordinates we find that these fields are continuous but possess only a finite density of degrees of freedom similar to fields on lattices as a special case we recover the shannon sampling theorem of information theory

rotation invariant moment problems an important theorem of marcel riesz cf 14 states that the polynomials are dense in l2 x when x is a determinate measure on the real line in the indeterminate case riesz also characterized the measures x for which the polynomials are dense in l2 they are the so called nevanlinna extremal measures introduced in nevanlinna 11 it does not seem to be known whether the polynomials are dense in l2 g when x is a determinate measure on r d d 1 cf the expository paper by fuglede 7 as well as the research problems book 8 p 529 where devinatz poses the problem as question 1 and ascribes it to the physicist john challifour 1978 in this paper we shall settle the question in the negative there exist rotation invariant measures on r d d 1 which are determinate but for which the polynomials are not dense in l2 p such measures x are necessarily of the following very special form

the index of determinacy for measures and the norm of orthonormal polynomials for determinate measures having moments of every order we define and study an index of determinacy which checks the stability of determinacy under multiplication by even powers of it z for z a complex number using this index of determinacy we solve the problem of determining for which z e c the sequence p m z n m e n belongs to t2 where pn n is the sequence of orthonormal polynomials associated with the measure u

a queueing model and a set of orthogonal polynomials a single serving queueing model is studied where potential customers are discouraged at the rate n qn 0 q 1 n is the queue length the serving rate is n 1 qn n 0 1 the spectral function is computed and the corresponding set of orthogonal polynomials is studied in detail the slightly more general model with n qn 1 bqn n 1 qn 1 bqn and the analogous orthogonal polynomials are also investigated in both cases a method developed by pollaczek is used which has been used very successfully to study new sets of orthogonal polynomials by askey and ismail

asymptotic behaviour and cyclic properties of weighted shifts on directed trees abstract in this paper we investigate a new class of bounded operators called weighted shifts on directed trees introduced recently in 11 this class is a natural generalization of the so called weighted bilateral unilateral and backward shift operators in the first part of the paper we calculate the asymptotic limit and the isometric asymptote of a contractive weighted shift on a directed tree and that of the adjoint then we use the asymptotic behaviour and similarity properties in order to obtain cyclicity results we also show that a weighted backward shift operator is cyclic if and only if there is at most one zero weight

spectral theory for borel sets in rn of finite measure abstract let be a pair of subsets in r n such that has finite positive lebesgue measure the pair is called a spectral pair if the functions e i x for form an orthogonal total family in l 2 i e when restricted to our present work continues earlier papers on simultaneous diagonalization of vector fields for the special case when is also assumed open however the setting here is more general and the results are stated in the measure theoretic category in considering fundamental domains for lattices for example we allow distinct lattice point translates of the domain to overlap on sets of measure zero rather than the traditional condition of empty overlap two classes of examples of spectral pairs are known fundamental domains and simple factors the latter may be identified in terms of a certain finite group action we show that every spectral pair can be factored in the sense of cartesian products as a product of two pairs of lower dimension where the first factor is a fundamental domain and the second a simple factor the dimensions add a simple factor yields in a natural way a finite covering of an associated compact torus but not every such covering corresponds to a spectral pair we give a complete spectral characterization of the finite coverings and identify those which correspond to simple factors the latter identification is phrased in terms of generators and relations for certain c algebras which are analogous to but different from algebras studied earlier by cuntz and arveson

vibration modeling of structural fuzzy with continuous boundary from experiments it is well known that the vibration response of a main structure with many attached substructures often shows more damping than structural losses in the components can account for in practice these substructures which are not attached in an entirely rigid manner behave like a multitude of different sprung masses each strongly resisting any motion of the main structure master at their base antiresonance the theory of structural fuzzy is intended for modeling such high damping in the present article the theory of fuzzy structures is briefly outlined and a method of modeling fuzzy substructures examined this is done by new derivations and physical interpretations are provided further the method is extended and simplified by introducing a simple deterministic approach to determine the boundary impedance of the structural fuzzy by using this new approach the damping effect of the fuzzy with spatial memory is demonstrated by numerical simulations of a main beam structure with fuz

commutative algebras of unbounded operators abstract we consider algebras u of unbounded operators defined on a common invariant dense domain d in a hilbert space h we assume that u is generated by a finite number of operators s1 sd satisfying the inequality x s x x s x x 0 for all finite sets of vectors x indexed by 1 d i 0 1 1 i d where s s 1 1 s d d and denotes the inner product in h we show that every such algebra dilates to a commutative algebra in a generally bigger hilbert space the latter algebra is generated by commuting formally normal extension operators n1 nd such that sjx njx x d 1 j d moreover the adjoint operators n j are represented as multiplication operators on a quotient of the space of d valued polynomials in complex variables z1 zd c d n j z j z d z j u z j z d if it is further assumed that d contains a dense space of vectors analytic for each of the operators sj then we prove that the nj s are essentially normal and there is a spectral measure e on the product of the spectrum of the closed normal operators n j such that n i f de and sjx jde x for x d as an application we consider representations of the canonical commutation relations in d degrees of freedom if p1 pd q1 qd denote the momentum resp position operators and sj pj iqj we show that s1 sd admits a representation as above we also show using our analytic vector theorem that the corresponding extension operators n 1 n d are commuting and normal for the schrodinger representation finally we calculate the spectral representation for the operators n j and prove absolute continuity and uniform multiplicity equal infinity the exposition of the paper begins with the case d 1 this is the unbounded version of the subnormal operators which have been studied extensively in the past in the case of bounded operators we stress the differences between the theory for the bounded and the unbounded case even in the case d 1 the applications of the unbounded theory are surprising

tiling the line with translates of one tile a region t is a closed subset of the real line of positive finite lebesgue measure which has a boundary of measure zero call a region t a tile if bbb r can be tiled by measure disjoint translates of t for a bounded tile all tilings of bbb r with its translates are periodic and there are finitely many translation equivalence classes of such tilings the main result of the paper is that for any tiling of bbb r by a bounded tile any two tiles in the tiling differ by a rational multiple of the minimal period of the tiling from it we deduce a structure theorem characterizing such tiles in terms of complementing sets for finite cyclic groups

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

simple vibration modeling of structural fuzzy with continuous boundary by including two dimensional spatial memory many complicated systems of practical interest consist basically of a well defined outer shell like master structure and a complicated internal structure with uncertain dynamic properties using the fuzzy structure theory for predicting audible frequency vibration the internal structure is considered as one or more fuzzy substructures that are known in some statistical sense only experiments have shown that such fuzzy substructures often introduce a damping in the master which is much higher than the structural losses account for a special method for modeling fuzzy substructures with a one dimensional continuous boundary was examined in a companion paper l friis and m ohlrich vibration modeling of structural fuzzy with continuous boundary j acoust soc am 123 718 728 2008 in the present paper this method is extended such that it allows modeling of fuzzy substructures with a two dimensional continuous boundary additionally a simple method for determining the so called equivalent cou

a model and numerical method in the medium frequency range for vibroacoustic predictions using the theory of structural fuzzy in linear dynamical analysis of complex mechanical systems the structural fuzzy is defined as the set of minor subsystems that are connected to the master structure but are not accessible by classical modeling the notion of master structure is presently extended to others elements such as an external dense compressible fluid strongly coupled with the primary structure for the low frequency lf dynamical analysis the modeling of the structural fuzzy is commonly made with a system of masses if the lf modeling of the structural fuzzy is applied in the medium frequency mf domain there are some large differences between calculations and experiment it is therefore necessary to take into account internal degrees of freedom of the structural fuzzy a global probabilistic modeling of the structural fuzzy is proposed to improve the calculated estimates of the mf vibrations into the master structure and of the far field radiated by itself in or out of context of the acoustic scattering this paper reviews the author s previous work and introduces the type ii probabilistic constitutive law in this paper 1 a probabilistic modeling of the structural fuzzy is presented 2 two probabilistic constitutive laws of the structural fuzzy are constructed 3 the modeling in the mf range for vibroacoustic predictions using theory of structural fuzzy is developed 4 the fuzzy solution in the mf range is studied and 5 numerical simulations on standard structures and on a submerged complex industrial structure are shown

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

a shimorin type analytic model on an annulus for left invertible operators and applications abstract a new analytic model for left invertible operators which extends both shimorin s analytic model for left invertible and analytic operators and gellar s model for bilateral weighted shift is introduced and investigated we show that a left invertible operator t which satisfies certain conditions can be modeled as a multiplication operator m z on a reproducing kernel hilbert space of vector valued analytic functions on an annulus or a disc a similar result for composition operators in l 2 spaces is established

comparison of commuting one parameter groups of isometries abstract let a s be two commuting strongly continuous one parametergroups of isometries on a banach space j with generators 5q and 5 andanalytic elements srff srff respectively then it is easy to show that if oais relatively bounded by 5 then srff c saf and in this paper we establishthe inverse implication for unitary one parameter groups on hubert spaces andfor one parameter groups of automorphisms of abelian c algebras it is notknown in general whether the inverse implication holds or not but it does nothold for one parameter semigroups of contractions 1 introduction our intention in this paper is to examine the extent to which the analyticelements determine a strongly continuous one parameter group of isometries ona banach space for example if if v are two one parameter unitary groups on the hubert space sv with analytic elements a jfia v and generators h k and if u commutes with v then we prove that s w u c s jv if

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

spectral sets whose spectrum is a lattice with a base abstract let l be a finite subset of euclidean d dimensional space r d and let s be a lattice in r d such that l l l l l s 0 a classification of all lebesgue measurable subsets of r d for which the functions e x exp i 2 x x l s l s l l s s form an orthogonal basis for l 2 is given in terms of geometric and combinatorial data the data is derived from l and s

on diffraction by aperiodic structures this paper gives a rigorous treatment of some aspects of diffraction by aperiodic structures such as quasicrystals it analyses diffraction in the limit of the infinite system through an appropriately defined autocorrelation the main results are a justification of the standard way of calculating the diffraction spectrum of tilings obtained by the projection method and a proof of a variation on a conjecture by bombieri and taylor

unitary representations of lie groups with reflection symmetry we consider the following class of unitary representations of some real lie groupgwhich has a matched pair of symmetries described as follows i supposeghas a period 2 automorphism and that the hilbert spaceh carries a unitary operatorjsuch thatj j i e selfsimilarity ii an added symmetry is implied ifh further contains a closed subspacek0having a certainorder covarianceproperty and satisfying thek0 restricted positivity v jv 0 v k0 where is the inner product inh from i ii we get an induced dual representation of an associated dual groupgc all three properties selfsimilarity order covariance and positivity are satisfied in a natural context whengis semisimple and hermitean but whengis the ax b group or the heisenberg group positivity is incompatible with the other two axioms for the infinite dimensional irreducible representations we describe a class ofg containing the latter two which admits a classification of the possible spacesk0 h satisfying the axioms of selfsimilarity and order covariance

extending positive definiteness the main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of semigroups to positive definite ones by specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems like complex two sided complex and multidimensional trigonometric moment problems in addition unbounded subnormality and existence of unitary power dilation of several contractions is treated as an application of our general scheme

transient energy exchange between a primary structure and a set of oscillators return time and apparent damping in this paper we examine the conditions that influence the return time the time it takes before energy returns from a set of satellite oscillators attached to a primary structure two methods are presented to estimate the return time one estimate is based on an analysis of the reaction force on a rigid base by a finite number of oscillators as compared with an infinite number of continuously distributed oscillators the result gives a lower bound estimate for the return time a more accurate estimation results from considering the dynamic behavior of a set of oscillators as waves in a waveguide such an analogy explains energy flow between a primary structure and the oscillators in terms of pseudowaves and shows that a nonlinear frequency distribution of the oscillators leads to pseudodispersive waves the resulting approximate expressions show the influence of the natural frequency distribution within the set of oscillators and of their number on the return time as compared with the asymptotic case of a continuous set with infinite oscillators in the paper we also introduce a new method based on a hilbert envelope to estimate the apparent damping loss factor of the primary structure during the return time considering transient energy flow from the primary structure before any energy reflects back from the attached oscillators the expressions developed for return time and damping factor show close agreement with direct numerical simulations the paper concludes with a discussion of the return time and its relation to apparent damping and optimum frequency distribution within a set of oscillators that maximize these quantities

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

spectral theory of finite volume domains in rn abstract let be an arbitrary open subset of r n of finite positive measure and assume the existence of a subset r n such that the exponential functions e exp i 1x1 nxn 1 n form an orthonormal basis for l 2 with normalized measure assume 0 and define subgroups k and a of r n by k 0 r n 2 z a a r n ua m u a m where ut is the unitary representation of r n on l 2 given by ute eit e t r n and where m is the multiplication algebra of l on l2 assume that a is discrete then there is a discrete subgroup d a of dimension n a fundamental domain d for d and finite sets of representers r r r each containing 0 r for a k in k0 and r for a k in a such that is disjoint union of translates of d a r a d neglecting null sets and r d0 if r is a set of representers for d a in d then r k is a translation set for i e r n direct sum neglecting null sets the case a r n corresponds to d d0 and k this last case corresponds in turn to a function theoretic assumption of forelli

estimation of fuzzy structure parameters for continuous junctions the fuzzy structure theory introduced 15 years ago is designed to predict the frequency response functions of structures and structural acoustic systems with structural complexity in the low and medium frequency ranges this paper constitutes a first validation of the fuzzy structure theory for continuous junctions between the master structure and the fuzzy substructures in addition a method to estimate the fuzzy structure parameters introduced in the fuzzy structure theory is presented and it is validated for the case of continuous junctions this validation obtained by numerical simulations opens the field of experimental identifications

on a unified mixture distribution in this article a new mixture distribution associated with fox wright generalized hypergeometric function has been studied which generalizes many mixture distributions investigated earlier by many authors some basic functions associated with the probability density function of the mixture distribution such as kth moments characteristic function and factorial moments are derived some special cases are also pointed out

a subnormal weighted shift on a directed tree whose nth power has trivial domain abstract it is shown that for any positive integer n there exists a subnormal weighted shift on a directed tree whose nth power is closed and densely defined while its n 1 th power has trivial domain similar result for composition operators in l 2 spaces is established

harmonic analysis and fractal limit measures induced by representations of a certain c algebra we describe a class of measurable subsets in rd such that l2 has an orthogonal basis of frequencies e x ei2 x x indexed by rd we show that such spectral pairs have a self similarity which may be used to generate associated fractal measures typically with cantor set support the hilbert space l2 does not have a total set of orthogonal frequencies but a harmonic analysis of may be built instead from a natural representation of the cuntz c algebra which is constructed from a pair of lattices supporting the given spectral pair we show conversely that such a pair may be reconstructed from a certain cuntz representation given to act on l2

spectral theory of commuting self adjoint partial differential operators let denote a connected and open subset of rn the existence of n commuting self adjoint operators h1 hn on l2 such that each hj is an extension of i xj acting on cc is shown to be equivalent to the existence of a measure on rn such that f tf the fourier transform of f is unitary from l2 onto it is shown that the support of can be chosen as a subgroup of rn iff h1 hn can be chosen such that the unitary groups generated by h1 hn act multiplicatively on l2 this happens iff after correction by a null set forms a system of representatives for the quotient of rn by some subgroup i e iff is essentially a fundamental domain

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

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

the heat semigroup and integrability of lie algebras abstract let du x 1 s t c t 1 2 0 denote a continuous representation u of a lie group g acting on a banach space b and s the semigroup generated by the closed laplacian associated with a basis of the lie algebra g in the derived representation du we prove there is a c 0 such that du x i s t c t 1 2 0 for all xi in the basis of g and we also prove that this property is characteristic for integrability of a lie algebra of operators satisfying the usual dissipativity requirements for generators of one parameter groups the basic estimate is established from bounds on the heat kernel associated with s

on unbounded bergman operators abstract this paper explores properties of the bergman operator on unbounded open subsets of the plane in addition to the characterization of the bounded commutant of such operators it proves the berger shaw theorem and gives some general criteria under which the operator and its self commutator are densely defined

subnormal operators whose adjoints have rich point spectrum a generalized version of the glauber klauder basic formula of quantum optics is shown to be valid for any cyclic subnormal operator s whose adjoint has a rich point spectrum p s in the sense that a semispectral measure of s vanishes on c p s it is exhibited that such operators always have analytic models the point spectrum of the adjoint of a subnormal operator which satisfies a generalized version of the glauber klauder formula is proved to be rich in the above sense

on a generalized mixture distribution in this paper we obtain a new mixture distribution which generalizes some other mixture distributions established earlier some basic functions associated with the probability density function of the mixture distribution such as kth moments characteristic function and factorial moments are computed further we obtain a three term recurrence relation for the established mixture distribution

the complex moment problem and subnormality a polar decomposition approach abstract it has been known that positive definiteness does not guarantee a bisequence to be a complex moment however it turns out that positive definite extendibility does theorems 1 and 22 and this is the main theme of this paper the main tool is generally understood polar decomposition to strengthen applicability of our approach we work out a criterion for positive definite extendibility in a fairly wide context theorems 9 and 29 all this enables us to prove characterizations of subnormality of unbounded operators having invariant domain theorems 37 and 39 and their further applications theorems 41 and 43 and a description of the complex moment problem on real algebraic curves theorems 52 and 56 the latter question is completed in the appendix in which we relate the complex moment problem to the two dimensional real one with emphasis on real algebraic sets