subdiffusive quantum transport for 3d hamiltonians with absolutely continuous spectra we exhibit a class of hamiltonians in dimension d 3 describing a quantum particle in an aperiodic medium with absolutely continuous spectrum and subdiffusive behavior the diffusion exponent which characterizes the time growth of the mean square displacement can be chosen slightly bigger than guarneri s lower bound these models are built out of 1d hamiltonians with well understood spectral and transport properties

the bishop phelps bollobas theorem for operators we prove the bishop phelps bollobas theorem for operators from an arbitrary banach space x into a banach space y whenever the range space has property of lindenstrauss we also characterize those banach spaces y for which the bishop phelps bollobas theorem holds for operators from 1 into y s everal examples of classes of such spaces are provided for instance the bishop phelps bollobas theorem holds when the range space is finite dimensional an l1 space for a finite measure a c k space for a compact hausdorff space k or a uniformly convex banach space

pure point spectrum for discrete almost periodic schrodinger operators the finite difference schrodinger operator on m is considered hu j left sum limits v 1 m d v 2 right u j frac 1 varepsilon q j u j u in ell 2 mathbb z m where sum limits v 1 m d v 2 is the difference laplacian inm dimensions for sufficiently small almost periodic potentialsq j are constructed such that the operatorh has only pure point spectrum the method is an inverse spectral procedure which is a modification of the kolmogorov arnol d moser technique

spectrum and diffusion for a class of tight binding models on hypercubes we propose a class of exactly solvable anisotropic tight binding models on an infinite dimensional hypercube the energy spectrum is computed analytically and is shown to be fractal and or absolutely continuous according to the value of the hopping parameters in both cases the spectral and diffusion exponents are derived the main result is that even if the spectrum is absolutely continuous the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models

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

orthogonal polynomials for minkowski s question mark function hermann minkowski introduced a function in 1904 which maps quadratic irrational numbers to rational numbers and this function is now known as minkowski s question mark function since minkowski used the notation x this function is a distribution function on 0 1 which defines a singular continuous measure with support 0 1 our interest is in the monic orthogonal polynomials p n n n for the minkowski measure and in particular in the behavior of the recurrence coefficients of the three term recurrence relation we will give some numerical experiments using the discretized stieltjes gautschi method with a discrete measure supported on the minkowski sequence we also explain how one can compute the moments of the minkowski measure and compute the recurrence coefficients using the chebyshev algorithm

singularly continuous spectrum of a self similar laplacian on the half line we investigate the spectrum of the self similar laplacian which generates the so called pq random walk on the integer half line using the method of spectral decimation we prove that the spectral type of the laplacian is singularly continuous whenever p 12 this serves as a toy model for generating singularly continuous spectrum which can be generalized to more complicated settings we hope it will provide more insight into fibonacci type and other weakly self similar models

bishop phelps bollobas property for certain spaces of operators abstract we characterize the banach spaces y for which certain subspaces of operators from l 1 into y have the bishop phelps bollobas property in terms of a geometric property of y namely ahsp this characterization applies to the spaces of compact and weakly compact operators new examples of banach spaces y with ahsp are provided we also obtain that certain ideals of asplund operators satisfy the bishop phelps bollobas property

the bishop phelps bollobas theorem fails for bilinear forms on l1 l1 abstract in this paper we show that the bishop phelps bollobas theorem fails for bilinear forms on l 1 l 1 while it holds for linear operators from l 1 to l

optimal biorthogonal wavelet decomposition of wire frame meshes using box splines and its application to the hierarchical coding of 3 d surfaces optimal mechanisms are determined for the hierarchical decomposition of wire frame surfaces generated by box splines a family of box splines with compact support suitable for the approximation of wire frames is first defined generated by arbitrary sampling matrices with integer eigenvalues for each such box spline the optimal positioning of the wire frame nodes is determined for each level of the hierarchical wire frame decomposition criterion of optimality is the minimization of the variance of the error difference between the original surface and its representation at each resolution level this is needed so as to ensure that the wire mesh produces at each resolution as close a replica of the original surface as possible several such combinations of box spline generated meshes and the corresponding optimal node lattice sequences are examined in detail with a view to practical application their specific application to the hierarchical coding of three dimensional 3 d wire meshes is experimentally evaluated

almost periodic jacobi matrices associated with julia sets for polynomials let be the jacobi matrix associated with polynomialt z of degreen 2 the spectrum of is the julia set associated witht z which in many cases is a cantor set let 1 denote the result of omitting the first row and column ofj then it is shown that the spectrum of 1 may be purely discrete

a lindenstrauss theorem for some classes of multilinear mappings abstract under some natural hypotheses we show that if a multilinear mapping belongs to some banach multilinear ideal then it can be approximated by multilinear mappings belonging to the same ideal all whose arens extensions attain their norms at the same point we prove a similar result for the class of symmetric multilinear mappings we see that the quantitative bollobas type version of these results fails in every multilinear ideal

meblin transforms associated with julia sets and physical applications we introduce the mellin transform of the balanced invariant measure associated to the julia set generated by a rational transformation we show that its analytic continuation is a meromorphic function the poles of which are on a semi infinite periodic lattice this allows one to have an understanding of the behavior of the measure near a repulsive fixed point trace identities corresponding to the fact that the analytically continued mellin transform vanishes at negative integers are derived for the polynomial case the quadratic map is first analyzed in detail and the analytic properties of the inverse of the green s function are exhibited of interest is the appearance of a dense set of spikes at dyadic points when the julia set is disconnected these results are used to study the residues of the mellin transform a certain number of physically interesting consequences are derived for the spectral dimensionality of quantum mechanical systems the excitation spectrum of which displays unusual oscillations the appearance of complex critical indices for thermodynamical systems is also discussed in the conclusion

kotani theory for one dimensional stochastic jacobi matrices we consider families of operators h on l2 given by h u n u n 1 u n 1 v n u n wherev is a stationary bounded ergodic sequence we prove analogs of kotani s results including that for a e ac h is the essential closure of the set ofe where e the lyaponov index vanishes and the result that ifv is non deterministic then ac is empty

2 d bauer factorization the extension to the 2 d case of the bauer formulation of the spectral factorization is given the relation to the 2 d generalization of the levinson algorithm by marzetta leads to a proof of the convergence of the method the problems of the practical implementation are discussed

orthogonality properties of iterated polynomial mappings we consider a measure defined on a complex contour and its associated orthogonal polynomials the action of a polynomial transformation on the measure and the transformation laws of the corresponding orthogonal polynomials are given iterating the transformation provides an invariant measure whose support is the julia set corresponding to the polynomial transformation it appears that up to a constant the iterated polynomials generated by the initial mapping form a subset of the invariant set of orthogonal polynomials which fulfill a three term recursion relation an algorithm is given to compute the coefficients of this recursion relation which can be interpreted as a linear extension of the iterative procedure

spectral behavior of quasi periodic potentials spectral properties of schrodinger operators of the typeh v where is the laplacian v a quasiperiodic potential and a coupling constant are developed v is taken to be finite sum of exponentials with generic frequencies for small a strong stability is shown on the other hand examples in the finite diffeence case are given for which a transition in the type of spectrum occurs as is increased

optimal pyramidal decomposition for progressive multidimensional signal coding using optimal quantizers optimal hierarchical coding is sought for progressive or scalable multidimensional signal transmission by minimizing the variance of the error difference between the original image and its lower resolution renditions the optimal according to the above criterion pyramidal coders are determined for images quantized using the optimal vector lloyd max quantizers a rigorous general statistical model of a vector lloyd max quantizer is used consisting of a linear time invariant filter followed by additive noise uncorrelated with the input given arbitrary analysis filters the optimal synthesis filters are found the optimal analysis filters are subsequently determined leading to formulas for globally optimal structures for pyramidal multidimensional signal decompositions these structures produce replicas of the original image which at lower resolutions retain as much similarity to the original as possible this is highly useful for the progressive coding of two or three dimensional 2 d or 3 d images needed in applications such as fast browsing through image databases furthermore the minimization of the variance of the error image leads to minimization of the variance of the quantization noise for this image and hence to its optimally efficient compression experimental results illustrate the implementation and performance of the optimal pyramids in application for the coding of still 2 d images

orthogonal polynomials of equilibrium measures supported on cantor sets the equilibrium measure of a compact set is a fundamental object in logarithmic potential theory we compute numerically this measure and its orthogonal polynomials when the compact set is a cantor set defined by an iterated function system we first construct sequences of discrete measures via the solution of large systems of non linear equations that converge weakly to the equilibrium measure successively we compute their jacobi matrices via standard procedures enhanced for the scope numerical estimates of the convergence rate to the limit jacobi matrix are provided which show stability and efficiency of the whole procedure as a companion result we also compute jacobi matrices in two other cases equilibrium measures on finite sets of intervals and balanced measures of iterated function systems these algorithms can reach large polynomial orders therefore we study the asymptotic behavior of the orthogonal polynomials and by a natural extension of the concept of regular root asymptotics we derive an efficient scheme for the computation of complex green s functions and of related conformal mappings

renormalization of random jacobi operators we construct a cantor set open image in new window of limit periodic jacobi operators having the spectrum on the julia setj of the quadratic mapz z2 e for large negative real numberse the density of states of each of these operators is equal to the unique equilibrium measure onj the jacobi operators in open image in new window are defined over the von neumann kakutani system a group translation on the compact topological group of dyadic integers the cantor set open image in new window is an attractor of the iterated function system built up by the two renormalisation maps l d 2 e d to prove the contraction property we use an explicit interpolation of the backlund transformations by toda flows we show that the attractor open image in new window is identical to the hull of the fixed pointl of

optimal pyramidal and subband decompositions for hierarchical coding of noisy and quantized images optimal hierarchical coding is sought for progressive or scalable image transmission by minimizing the variance of the error difference between the original image and its lower resolution renditions the optimal according to the above criterion pyramidal and subband image coders are determined for images subject to corruption by quantization or transmission noise given arbitrary analysis filters and assuming adequate knowledge of the noise statistics optimal synthesis filters are found the optimal analysis filters are subsequently determined leading to formulas for globally optimal structures for pyramidal and subband image decompositions experimental results illustrate the implementation and performance of the optimal coders

on the polynomial lindenstrauss theorem abstract under certain hypotheses on the banach space x we show that the set of n homogeneous polynomials from x to any dual space whose aron berner extensions are norm attaining is dense in the space of all continuous n homogeneous polynomials to this end we prove an integral formula for the duality between tensor products and polynomials we also exhibit examples of lorentz sequence spaces for which there is no polynomial bishop phelps theorem but our results apply finally we address quantitative versions in the sense of bollobas of these results

optimal construction of subband coders using lloyd max quantizers a new method is presented for the analysis of the effects of lloyd max quantization in subband filterbanks and for the optimal design of such filterbanks a rigorous statistical model of a vector lloyd max quantizer is established first consisting of a linear time invariant filter followed by additive noise uncorrelated with the input on the basis of this model an expression for this variance of the error of a subband coder using lloyd max quantizers is explicitly determined given analysis filters that statistically separate the subbands it is shown that this variance is minimized if the synthesis filters are chosen which mould achieve perfect reconstruction in lossless coding the globally optimum of such a filterbank minimizing the coder error variance is further obtained by proper choice of its analysis filters an alternative design method is also evaluated and optimized in this the errors correlated with the signal are set to zero leaving a random error residue uncorrelated with the signal this design method is optimized by choosing the analysis filters so as to minimize the random error variance the results are evaluated experimentally in the realistic setting of a logarithmically split subband image coding scheme

singular continuous spectrum for a class of almost periodic jacobi matrices we consider operators parametrized by a o on 2 with matrix ojy i o i fl o y with an cos 2ttcw 6 if ce is a liouville number and 2 we prove that for a e 0 the operator s spectral measures are all singular continuous we consider the operator on l2 z depending upon three parameters x a 0 1 x a 0 u n u n 1 u n 1 x cos 2iran 6 u n in this note we will sketch the proof of the following result whose detailed proof will appear elsewhere 3 theorem 1 fix a an irrational number obeying

spectral properties of one dimensional quasi crystals in this paper we prove that the one dimensional schrodinger operator onl 2 with potential given by upsilon n lambda chi 1 alpha 1 x n alpha alpha notin mathbb q has a cantor spectrum of zero lebesgue measure for any irrational and any 0 we can thus extend the kotani result on the absence of absolutely continuous spectrum for this model to all mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepge9fr xfr x frpewzqaaeaabigaciaacaqabeaadaqaaqaaaoqaaiaadihaiiaacq wfiiiztuudjxwak1uy0hmmaehbfv3yslgzg0uy0hgiud3bagqbbiab nj8ubaa 4628 x in mathbb t

2 d wilson spectral factorization g wilson s method of spectral factorization 1969 is considered for generalization to the two dimensional 2 d case for practical implementation finite order approximants to the 2 d spectral factors of infinite order are obtained although stability or convergence cannot be guaranteed in general justifications are given for the success of the proposed generalization illustrative examples are given to support the conclusions

moments of balanced measures on julia sets by a theorem of s demko there exists a balanced measure on the julia set of an arbitrary nonlinear rational transformation on the riemann sphere it is proved here that if the transformation admits an attractive or indifferent cycle then there is a point with respect to which all the moments of a balanced measure exist moreover these moments can be calculated exactly an explicit balanced measure is exhibited in an example where the julia set is the whole sphere and for which the moments with respect to any point do not all exist 1 introduction the julia set for a nonlinear rational transformation on the riemann sphere is the closure of the set of all repulsive cycles of the transformation br fa j the location or distribution of the set is of interest in the theory of iterated maps and it may be characterized by an associated invariant measure in this paper we extend previous results by showing that when there is an attractive or indifferent cycle certain moments of such a measure exist and can be calculated exactly from the rational transformation this means for example that when the julia set is contained strictly in the real line all of the orthogonal polynomials on the set can be calculated as can the entries of the corresponding infinite dimensional jacobi matrices the latter are of the type which have recently been shown to furnish model schrodinger equations for crystals with almost periodic potentials bbm this leads us to the following speculation which provides one reason for our interest in the present topic we note first the frequent occurrence in the physical universe of objects steady state systems which are fractals from some point of

construction of optimal subband coders using optimized and optimal quantizers a method is presented for the optimization of arbitrary quantizers by use of a compensating postfilter it is shown that the resulting optimized quantizers fit the model of a linear time invariant filter followed by additive noise uncorrelated with the input which also characterizes the optimal lloyd max quantizers on the basis of this model an expression for the variance of the error of a subband coder using optimized quantizers is explicitly determined given analysis filters which statistically separate the subbands it is shown that this variance is minimized if these synthesis filters are chosen which would achieve perfect reconstruction in lossless coding the globally optimum filter bank minimizing the coder error variance is further obtained by proper choice of its analysis filters a novel method for the determination of optimal bit allocation to subbands of the filter banks with optimized quantizers is also developed the results are evaluated experimentally by comparison of the optimum uniformly split subband image coding scheme to classical logarithmically split filter bank wavelet coding methods

on the approximate factorization of 2 d polynomials a method is presented for the approximate factorization of unfactorable bivariate polynomials an efficient iterative algorithm is developed to minimize an appropriate criterion the basic ideas can be easily extended to the case of polynomials in more than two independent variables an example is presented to illustrate the utility of the method

two sided polynomial ideals on banach spaces abstract classes of homogeneous polynomials between banach spaces have been studied in the last three decades from the perspective of the stability with respect to the composition of a homogeneous polynomial with linear operators in an attempt to explore the underlying nonlinearity in a more consistent way and to bring the subject closer to its roots in complex analysis and also taking into account recent results in the field in this paper we propose the study of classes of homogeneous polynomials that are stable under the composition with homogeneous polynomials

hypercyclic convolution operators on frechet spaces of analytic functions a result of godefroy and shapiro states that the convolution operators on the space of entire functions on c n which are not multiples of identity are hypercyclic analogues of this result have appeared for some spaces of holomorphic functions on a banach space in this work we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators some known results come out as particular cases of this setting we also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the schatten von neumann class

the rotation number for finite difference operators and its properties we discuss a rotation number for second order finite difference operators ifk denotes the integrated density of states thenk 2 for almost periodic operators k is proved to lie in the frequency module whenever is outside the spectrum this yields a labelling of the gaps of the spectrum

norm attaining bilinear forms onl1 0 1 abstract we show that the set of norm attaining bilinear forms onl1 0 1 is not dense in the space of all continuous bilinear forms

orthogonal polynomials on several intervals via a polynomial mapping starting from a sequence pn x no of orthogonal polynomials with an orthogonality measure yurj supported on eo c 1 1 we construct a new sequence p x fi of orthogonal polynomials on t 1 eq t is a polynomial of degree tv with an orthogonality measure i that is related to no if eo 1 1 then e t 1 l l will in general consist of tv intervals we give explicit formulas relating pn x fi and pn x fio and show how the recurrence coefficients in the three term recurrence formulas for these orthogonal polynomials are related if one chooses t to be a chebyshev polynomial of the first kind then one gets sieved orthogonal polynomials

a multilinear lindenstrauss theorem abstract we show that the set of n linear mappings on a product of n banach spaces such that all their arens extensions attain their norms at the same element is norm dense in the space of all bounded n linear mappings