sampling and interpolation in large bergman and fock spaces we obtain sampling and interpolation theorems in weighted spaces of analytic functions for radial weights of arbitrary more rapid than polynomial growth we give an application to invariant subspaces of arbitrary index in large weighted bergman spaces

guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications in this paper we discuss with guaranteed a priori and a posteriori error estimates of finite element approximations for not necessarily coercive linear second order dirichlet problems here guaranteed means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form using the invertibility condition of concerning elliptic operator guaranteed a priori and a posteriori error estimates are formulated this kind of estimates plays essential and important roles in the numerical verification of solutions for nonlinear elliptic problems several numerical examples that confirm the actual effectiveness of the method are presented

some sufficient conditions for the division property of invariant subspaces in weighted bergman spaces the authors consider weighted bergman spaces of holomorphic l sp p integrable functions with respect to certain borel measures on a bounded plane region a closed subspace scr m of such a space is said to be invariant if z scr m subset scr m in the case of the standard bergman space of the unit disk with p 2 the authors proved in a recent joint paper with c sundberg acta math 177 1996 no 2 275 310 mr1440934 98a 46034 that every invariant subspace scr m is generated by a wandering subspace scr m ominus z scr m for the shift operator thus obtaining an analogue of the celebrated theorem of beurling an invariant space is said to have the division property if the quotient space scr m z lambda scr m is one dimensional for any lambda in the domain under certain additional hypotheses this is equivalent to the codimension one property studied earlier by s richter h hedenmalm k seip and others the main results of this paper are various sufficient conditions for an invariant subspace to have the division property in terms of the local boundary behavior of the functions in the subspace a function f analytic in the unit disc is said to be locally nevanlinna near a point lambda on the unit circle if the subharmonic function log f has a harmonic majorant in the carleson type set obtained by intersecting the unit disk with some disc centered at lambda the authors show that an invariant subspace scr m of the standard bergman space a sp p sb alpha with radial weights 1 z sp 2 sp alpha p ge 1 alpha 1 possesses the division property if some nonzero function f in the subspace is locally nevanlinna at a boundary point they observe that given an invariant subspace scr m which does not have the division property it will always contain two functions such that the space they generate does not have it either it is therefore a question of interest to determine under what conditions the space generated by two functions will possess this property the authors prove the following theorem let 1 le p infty 1 r 1 s 1 p and let f and g be two nonzero functions in a sp p such that f is locally r integrable and g is locally s integrable both in a neighborhood of a boundary point of the disc then the closed linear span of the cyclic invariant subspaces generated by f and by g has the division property an example is also given based on the earlier results of hedenmalm and seip which shows that the theorem is in a way sharp for p 2 the main results also have some interesting corollaries listed in the paper less

random weighted shifts abstract in this paper we initiate the study of a fundamental yet untapped random model of non selfadjoint bounded linear operators acting on a separable complex hilbert space we replace the weights w n 1 in the classical unilateral shift t defined as t e n w n e n 1 where e n n 1 form an orthonormal basis of a complex hilbert space by a sequence of i i d random variables x n n 1 that is w n x n this paper answers basic questions concerning such a model we propose that this model can be studied in comparison with the classical hardy bergman dirichlet spaces in function theoretic operator theory we calculate the spectra and determine their fine structures section 3 we classify the samples up to four equivalence relationships section 4 we introduce a family of random hardy spaces and determine the growth rate of the coefficients of analytic functions in these spaces section 5 we compare them with three types of classical operators section 6 this is achieved in the form of generalized von neumann inequalities the invariant subspaces are shown to admit arbitrarily large indices and their semi invariant subspaces model arbitrary contractions almost surely we discuss a beurling type theorem section 7 we determine various non selfadjoint algebras generated by t section 8 their dynamical properties are clarified section 9 their iterated aluthge transforms are shown to converge section 10 in summary they provide a new random model from the viewpoint of probability theory and they provide a new class of analytic functional hilbert spaces from the viewpoint of operator theory the technical novelty in this paper is that the methodology used draws from three largely separate sources probability theory functional hilbert spaces and the approximation theory of bounded operators

an alternative approach to norm bound computation for inverses of linear operators in hilbert spaces abstract in the present paper we propose a computer assisted procedure to prove the invertibility of a linear operator in a hilbert space and to compute a verified norm bound of its inverse a number of the authors have previously proposed two verification approaches that are based on projection and constructive a priori error estimates the approach of the present paper is expected to bridge the gap between the two previous procedures in actual numerical verifications several verification examples that confirm the actual effectiveness of the proposed procedure are reported

a combined integro modal approach for predicting acoustic properties of irregular shaped cavities an integro modal approach is presented in this paper for computing the acoustic properties of irregular shaped cavities the method consists of discretizing the whole cavity into a series of subcavities whose acoustic pressure is decomposed either over a modal basis of regular subcavities or over that of the bounding cavities in the case of irregular shaped boundaries an integral formulation is then established to ensure continuity of both pressure and velocity between adjacent subcavities using a membrane with zero mass and stiffness to some extent the method provides a combined approach retaining the advantages of both the acoustoelastic method aem and the green s function method gfm numerical and experimental results are presented demonstrating the efficiency and accuracy of the suggested technique comparisons with other existing methods are also made it is shown that good accuracy on the computation of cavity modes can be obtained using a very limited number of subcavities

a domain decomposition method for analyzing a coupling between multiple acoustical spaces l this letter presents a domain decomposition method to predict the acoustic characteristics of an arbitrary enclosure made up of any number of sub spaces while the lagrange multiplier technique usually has good performance for conditional extremum problems the present method avoids involving extra coupling parameters and theoretically ensures the continuity conditions of both sound pressure and particle velocity at the coupling interface comparisons with the finite element results illustrate the accuracy and efficiency of the present predictions and the effect of coupling parameters between sub spaces on the natural frequencies and mode shapes of the overall enclosure is revealed

a discontinuous galerkin method for the wave equation abstract we present a new discontinuous galerkin method for solving the second order wave equation using the standard continuous finite element method in space and a discontinuous method in time directly applied to second order ode systems we prove several optimal a priori error estimates in space time norms for this new method and show that it can be more efficient than existing methods we also write the leading term of the local discretization error in terms of lobatto polynomials in space and jacobi polynomials in time which leads to superconvergence points on each space time cell we discuss how to apply our results to construct efficient and asymptotically exact a posteriori estimates for space time discretization errors numerical results are in agreement with theory

some lower bound estimates for resolvents of a compact operator on an infinite dimensional hilbert space abstract this paper presents some lower estimates for resolvents of a compact operator a on an infinite dimensional hilbert space usually upper estimates for resolvents are known under suitable conditions but lower estimates are not known these estimates enable us to calculate suitability results for approximation of a resolvent

a biharmonic maximum principle for hyperbolic surfaces let w be a simply connected two dimensional riemannian manifold with a cysmooth metric ds we can always introduce local isothermal coordinates near any point of w that is such coordinates x y that the metric is represented in the form ds x y 1 4 o x y dx dy for some positive weight function o and since w is orientable as a two dimensional simply connected manifold these local isothermal coordinates can serve as conformal charts for a complex structure on w see 1 pp 124 126 the k be uniformization theorem then says that w is conformally equivalent to one of the three sets the riemann sphere s 1 4 cw fyg the complex plane c or the open unit disk d this equivalence together with the choice of isothermal coordinates allows us to identify w with one of the above three sets w supplied with the isothermal riemannian metric

large bergman spaces invertibility cyclicity and subspaces of arbitrary index in a wide class of weighted bergman spaces we construct invertible non cyclic elements these are then used to produce z invariant subspaces of index higher than one in addition these elements generate non trivial bilaterally invariant subspaces in anti symmetrically weighted hilbert spaces of sequences

norm bound computation for inverses of linear operators in hilbert spaces abstract this paper presents a computer assisted procedure to prove the invertibility of a linear operator which is the sum of an unbounded bijective and a bounded operator in a hilbert space and to compute a bound for the norm of its inverse by using some projection and constructive a priori error estimates the invertibility condition together with the norm computation is formulated as an inequality based upon a method originally developed by the authors for obtaining existence and enclosure results for nonlinear partial differential equations several examples which confirm the actual effectiveness of the procedure are reported

numerical verification of existence and inclusion of solutions for nonlinear operator equations abstract nonlinear operator equations of the type f u lu nu 0 u d l are considered where l is a closed linear operator from a banach space x to another banach space y and n a nonlinear operator from x to y a method is presented for numerical verification and inclusion of solutions for the equations as an example the existence of a periodic solution is proved for the duffing equation

a new formulation using the schur complement for the numerical existence proof of solutions to elliptic problems without direct estimation for an inverse of the linearized operator infinite dimensional newton methods can be effectively used to derive numerical proofs of the existence of solutions to partial differential equations pdes in computer assisted proofs of pdes the original problem is transformed into the infinite dimensional newton type fixed point equation w mathcal l 1 mathcal f hat u mathcal l 1 mathcal g w where mathcal l is a linearized operator mathcal f hat u is a residual and mathcal g w is a nonlinear term therefore the estimations of vert mathcal l 1 mathcal f hat u vert and vert mathcal l 1 mathcal g w vert play major roles in the verification procedures in this paper using a similar concept to block gaussian elimination and its corresponding schur complement for matrix problems we represent the inverse operator mathcal l 1 as an infinite dimensional operator matrix that can be decomposed into two parts finite dimensional and infinite dimensional this operator matrix yields a new effective realization of the infinite dimensional newton method which enables a more efficient verification procedure compared with existing nakao s methods for the solution of elliptic pdes we present some numerical examples that confirm the usefulness of the proposed method related results obtained from the representation of the operator matrix as mathcal l 1 are presented in the appendix

an invariant subspace of the bergman space having the codimension two property nutzungsbedingungen digizeitschriften e v gewahrt ein nicht exklusives nicht ubertragbares personliches und beschranktes recht auf nutzung dieses dokuments dieses dokument ist ausschlieslich fur den personlichen nicht kommerziellen gebrauch bestimmt das copyright bleibt bei den herausgebern oder sonstigen rechteinhabern als nutzer sind sie sind nicht dazu berechtigt eine lizenz zu ubertragen zu transferieren oder an dritte weiter zu geben die nutzung stellt keine ubertragung des eigentumsrechts an diesem dokument dar und gilt vorbehaltlich der folgenden einschrankungen sie mussen auf samtlichen kopien dieses dokuments alle urheberrechtshinweise und sonstigen hinweise auf gesetzlichen schutz beibehalten und sie durfen dieses dokument nicht in irgend einer weise abandern noch durfen sie dieses dokument fur offentliche oder kommerzielle zwecke vervielfaltigen offentlich ausstellen auffuhren vertreiben oder anderweitig nutzen es sei denn es liegt ihnen eine schriftliche genehmigung von digizeitschriften e v und vom herausgeber oder sonstigen rechteinhaber vor mit dem gebrauch von digizeitschriften e v und der verwendung dieses dokuments erkennen sie die nutzungsbedingungen an

nontangential limits in pt µ spaces and the index of invariant subgroups let mu be a finite positive measure on the closed disk d over bar in the complex plane let 1 t infinity and let p t mu denote the closure of the analytic polynomials in l t mu we suppose that d is the set of analytic bounded point evaluations for p t mu and that p t mu contains no nontrivial characteristic functions it is then known that the restriction of mu to partial derivative d must be of the form h vertical bar dz vertical bar we prove that every function f is an element of p t mu has nontangential limits at h vertical bar dz vertical bar almost every point of partial derivative d and the resulting boundary function agrees with f as an element of l t h vertical bar dz vertical bar our proof combines methods from james e thomson s proof of the existence of bounded point evaluations for p t mu whenever p t mu not equal l t mu with xavier tolsa s remarkable recent results on analytic capacity these methods allow us to refine thomson s results somewhat in fact for a general compactly supported measure nu in the complex plane we are able to describe locations of bounded point evaluations for p t nu in terms of the cauchy transform of an annihilating measure as a consequence of our result we answer in the affirmative a conjecture of conway and yang we show that for 1 t infinity dim m zm 1 for every nonzero invariant subspace m of p t mu if and only if h not equal 0 we also investigate the boundary behaviour of the functions in p t mu near the points z is an element of partial derivative d where h z 0 in particular for 1 t infinity we show that there are interpolating sequences for p t mu that accumulate nontangentially almost everywhere on z h z 0 less

linear graph transformations on spaces of analytic functions let h be a hilbert space of analytic functions with multiplier algebra m h and let m f t 1 f t n 1 f f is an element of d be an invariant graph subspace for m h n here n 2 d subset of h is a vector subspace t i d h are linear transformations that commute with each multiplication operator m phi is an element of m h and m is closed in h n in this paper we investigate the existence of non trivial common invariant subspaces of operator algebras of the type a m a is an element of b h ad subset of d at i f t i af for all f is an element of d in particular for the bergman space l 0 2 we exhibit examples of invariant graph subspaces of fiber dimension 2 such that a m does not have any nontrivial invariant subspaces that are defined by linear relations of the graph transformations for m c 2015 elsevier inc all rights reserved less

elasto acoustic and acoustic acoustic coupling on non matching grids flexible discretization techniques for the approximative solution of coupled wave propagation problems are investigated focussing on aero acoustic and elasto acoustic coupling in particular the advantages of using non matching grids are presented when one subregion has to be resolved by a substantially finer grid than the other subregion for the elasto acoustic coupling the problem formulation remains essentially the same as for the matching situation while for the aero acoustic coupling the formulation is enhanced with lagrange multipliers within the framework of mortar finite element methods several numerical examples are presented to demonstrate the flexibility and applicability of the approach copyright 2006 john wiley sons ltd

shift invariant subspaces with arbitrary indices in lp spaces we construct right shift invariant subspaces of index n 1 n in lp spaces 2 p and in weighted lp spaces

on the index of invariant subspaces in hilbert spaces of vector valued analytic functions abstract let h be a hilbert space of analytic functions on the unit disc d with m z 1 where m z denotes the operator of multiplication by the identity function on d under certain conditions on h it has been shown by aleman richter and sundberg that all invariant subspaces have index 1 if and only if lim k m z k f 0 for all f h f 0 a aleman s richter c sundberg analytic contractions and non tangential limits trans amer math soc 359 7 2007 3369 3407 we show that the natural counterpart to this statement in hilbert spaces of c n valued analytic functions is false and prove a correct generalization of the theorem in doing so we obtain new information on the boundary behavior of functions in such spaces thereby improving the main result of m carlsson boundary behavior in hilbert spaces of vector valued analytic functions j funct anal 247 1 2007

bounded point evaluations for rationally multicyclic subnormal operators abstract let s be a pure bounded rationally multicyclic subnormal operator on a separable complex hilbert space h and let m z be the minimal normal extension on a separable complex hilbert space k containing h let b p e s be the set of bounded point evaluations and let a b p e s be the set of analytic bounded point evaluations we show a b p e s b p e s i n t s the result affirmatively answers a question asked by j b conway concerning the equality of the interior of b p e s and a b p e s for a rationally multicyclic subnormal operator s as a result if 0 i n t s and d i m k e r s 0 n where n is the minimal number of cyclic vectors for s then the range of s 0 is closed hence 0 s e s

estimation of interpolation error constants for the p0 and p1 triangular finite elements abstract we give some fundamental results on the error constants for the piecewise constant interpolation function and the piecewise linear one over triangles for the piecewise linear one we mainly analyze the conforming case but some results are also given for the non conforming case we obtain explicit relations for the dependence of such error constants on the geometric parameters of triangles in particular we explicitly determine the babuska aziz constant which plays an essential role in the interpolation error estimation of the linear triangular finite element the equation for determination is the transcendental equation tan 0 so that the solution can be numerically obtained with desired accuracy and verification such highly accurate approximate values for the constant as well as estimates for other constants can be widely used for a priori and a posteriori error estimations in adaptive computation and numerical verification of finite element solutions