isospectral flows related to frobenius stickelberger thiele polynomials the isospectral deformations of the frobenius stickelberger thiele fst polynomials introduced in spiridonov et al commun math phys 272 139 165 2007 are studied for a specific choice of the deformation of the spectral measure one is led to an integrable lattice fst lattice which is indeed an isospectral flow connected with a generalized eigenvalue problem in the second part of the paper the spectral problem used previously in the study of the modified camassa holm mch peakon lattice is interpreted in terms of the fst polynomials together with the associated fst polynomials resulting in a map from the mch peakon lattice to a negative flow of the finite fst lattice furthermore it is pointed out that the degenerate case of the finite fst lattice unexpectedly maps to the interlacing peakon ode system associated with the two component mch equation studied in chang et al adv math 299 1 35 2016

toda type differential equations for the recurrence coefficients of orthogonal polynomials and freud transformation transformations of the measure of orthogonality for orthogonal polynomials namely freud transformations are considered jacobi matrix of the recurrence coefficients of orthogonal polynomials possesses an isospectral deformation under these transformations dynamics of the coefficients are described by generalized toda equations the classical toda lattice equations are the simplest special case of dynamics of the coefficients under the freud transformation of the measure of orthogonality also dynamics of hankel determinants its minors and other notions corresponding to the orthogonal polynomials are studied

deformed laguerre hahn orthogonal polynomials on the real line abstract one derives discrete dynamical systems related to laguerre hahn orthogonal polynomials one studies deformations of the recurrence relation coefficients of the orthogonal polynomials under a t dependence on the coefficients of the riccati differential equation for the related stieltjes function

a characterization of decentralized fixed modes in terms of transmission zeros a simple development is given to show that a linear time invariant plant has a decentralized fixed mode at if and only if is a transmission zero of certain subsystems of the plant

stabilization of a class of slow fast control systems at non hyperbolic points in this document we deal with the local asymptotic stabilization problem of a class of slow fastsystems or singularly perturbed ordinary differential equations the systems studied here have the following properties 1 they have one fast and an arbitrary number of slow variables and 2 they have a non hyperbolic singularity at the origin of arbitrary degeneracy our goal is to stabilize such a point the presence of the aforementioned singularity complicates the analysis and the controller design in particular the classical theory of singular perturbations cannot be used we propose a novel design based on geometric desingularization which allows the stabilization of a non hyperbolic point of singularly perturbed control systems our results are exemplified on a didactic example and on an electric circuit

orthogonal polynomials and measures on the unit circle the geronimus transformations in this paper we analyze a perturbation of a nontrivial positive measure supported on the unit circle this perturbation is the inverse of the christoffel transformation and is called the geronimus transformation we study the corresponding sequences of monic orthogonal polynomials as well as the connection between the associated hessenberg matrices finally we show an example of this kind of transformation

the split levinson algorithm the classical levinson algorithm for computing the predictor polynomial relative to a real positive definite toeplitz matrix is shown to be redundant in complexity it can be broken down into two simpler algorithms either of which needs only to be processed this result can be interpreted in the framework of the theory of orthogonal polynomials on the real line as follows the symmetric and antisymmetric parts of the predictors relative to the sequence of toeplitz matrices constitute two families of polynomials orthogonal on the interval 1 1 with respect to some even weight functions it turns out that the recurrence relations for these orthogonal polynomials can be used efficiently to compute the desired predictor the resulting split levinson algorithm requires roughly one half the number of multiplications and the same number of additions as the classical levinson algorithm a simple derivation of cybenko s method for computing the pisarenko frequencies is obtained from the recurrence relations underlying the split levinson algorithm

adaptive dynamic surface control for stabilization of parametric strict feedback nonlinear systems with unknown time delays the robust stabilization method via the dynamic surface control dsc is proposed for uncertain nonlinear systems with unknown time delays in parametric strict feedback form that is the dsc technique is extended to state time delay nonlinear systems with linear parametric uncertainties the proposed control system can overcome not only the problem of ldquoexplosion of complexityrdquo inherent in the backstepping design method but also the uncertainties of the unknown time delays by choosing appropriate lyapunov krasovskii functionals in addition we prove that all the signals in the closed loop system are semiglobally uniformly bounded finally an example is provided to illustrate the effectiveness of the proposed control system

adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics in this paper the problems of stability and tracking control for a class of large scale nonlinear systems with unmodeled dynamics are addressed by designing the decentralized adaptive fuzzy output feedback approach because the dynamic surface control technique is introduced the designed controllers can avoid the issue of explosion of complexity which comes from the traditional backstepping design procedure that deals with large scale nonlinear systems with unmodeled dynamics in addition a reduced order observer is designed to estimate those immeasurable states based on the lyapunov stability method it is proven that all the signals in the closed loop system are bounded and the system outputs track the reference signals to a small neighborhood of the origin by choosing the design parameters appropriately the simulation examples are given to verify the effectiveness of the proposed techniques

schur flow for orthogonal polynomials on the unit circle and its integrable discretization a one parameter deformation of the measure of orthogonality for orthogonal polynomials on the unit circle is considered the corresponding dynamics of the schur parameters of the orthogonal polynomials is shown to be characterized by the complex semi discrete modified kdv equation namely the schur flow a discrete analogue of the miura transformation is found an integrable discretization of the schur flow enables us to compute a pade approximation of the caratheodory functions or equivalently to compute a perron caratheodory continued fraction in a polynomial time

characterizations of δ volterra lattice a symmetric orthogonal polynomials interpretation abstract in this paper we introduce the volterra lattice which is interpreted in terms of symmetric orthogonal polynomials it is shown that the measure of orthogonality associated with these systems of orthogonal polynomials evolves in t like 1 x 2 1 t x where is a given positive borel measure moreover the volterra lattice is related to the toda lattice from miura or backlund transformations the main ingredients are orthogonal polynomials which satisfy an appell condition with respect to the forward difference operator and the characterization of the point spectrum of a jacobian operator that satisfies a volterra equation lax type theorem we also provide an explicit example of solutions of volterra and toda lattices and connect this example with the results presented in the paper

inversion of a tridiagonal jacobi matrix abstract a formula for the inverse of a general tridiagonal matrix is given in terms of the principal minors

time complexity of decentralized fixed mode verification given an interconnected system this note is concerned with the time complexity of verifying whether an unrepeated mode of the system is a decentralized fixed mode dfm it is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system it is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication this work concludes that the identification of distinct dfms by means of a deterministic algorithm rather than a randomized one is computationally very easy although the existing algorithms for solving this problem would wrongly imply that it is cumbersome this note provides not only a complexity analysis but also an efficient algorithm for tackling the underlying problem

dynamics and interpretation of some integrable systems via multiple orthogonal polynomials high order non symmetric difference operators with complex coefficients are considered the correspondence between dynamics of the coefficients of the operator defined by a lax pair and its resolvent function is established the method of investigation is based on the analysis of the moments for the operator the solution of a discrete dynamical system is studied we give explicit expressions for the resolvent function and under some conditions the representation of the vector of functionals associated with the solution for the integrable systems

composite learning from adaptive dynamic surface control in the conventional adaptive control a stringent condition named persistent excitation pe must be satisfied to guarantee parameter convergence this technical note focuses on adaptive dynamic surface control for a class of strict feedback nonlinear systems with parametric uncertainties where a novel technique coined composite learning is developed to guarantee parameter convergence without the pe condition in the composite learning online recorded data together with instantaneous data are applied to generate prediction errors and both tracking errors and prediction errors are utilized to update parametric estimates the proposed approach is also extended to an output feedback case by using a nonlinear separation principle the distinctive feature of the composite learning is that parameter convergence can be guaranteed by an interval excitation condition which is much weaker than the pe condition such that the control performance can be improved from practical asymptotic stability to practical exponential stability an illustrative example is used for verifying effectiveness of the proposed approach

decentralized stabilization and pole assignment for general proper systems considered is the problem of finding existence conditions and a controller synthesis procedure using decentralized control for assigning the poles of a linear time invariant proper system described by a state space model c a b d where no assumption is made regarding the structure of d this problem has direct application to the decentralized stabilization problem decentralized robust servomechanism problem etc and is a nontrivial extension to the standard decentralized problem where it is assumed that the direct feedthrough terms either are absent or have a block diagonal structure

structure relations for orthogonal polynomials on the unit circle structure relations for orthogonal polynomials with respect to hermitian linear functionals are studied firstly we prove that semi classical orthogonal polynomials satisfy structure relations of the following type k 0s1 n kpn s1 k k 0s2 n kzkpn 1 k k 0r1 n kpn s1 k 1 k 0r2 n kpn r2 k where s1 s2 r1 r2 are integers specified in the text pn is the reversed polynomial of pn pn 1 pn 1 n 1 and n k n k n k n k are complex numbers then we study the semi classical character of sequences of orthogonal polynomials rn pn connected through a structure relation of the following type k 0s1 n krn s1 k k 0s2 n krn s2 k k 0r1 n kpn r1 k 1 k 0r2 n kpn r2 k where the integers s1 s2 r1 r2 satisfy some natural conditions specified in the text

lebesgue perturbation of a quasi definite hermitian functional the positive definite case abstract in this work we study the problem of orthogonality with respect to a sum of measures or functionals first we consider the case where one of the functionals is arbitrary and quasi definite and the other one is the lebesgue normalized functional next we study the sum of two positive measures the first one is arbitrary and the second one is the lebesgue normalized measure and we obtain some relevant properties concerning the new measure finally we consider the sum of a bernstein szeg measure and the lebesgue measure in this case we obtain more simple explicit algebraic relations as well as the relation between the corresponding szeg s functions

a characterization of classical and semiclassical orthogonal polynomials from their dual polynomials we study properties of the dual orthogonal polynomials op introduced by de boor and saff and present a new characterization of the classical and semiclassical op

orthogonal laurent polynomials on the unit circle extended cmv ordering and 2d toda type integrable hierarchies abstract we connect the theory of orthogonal laurent polynomials on the unit circle and the theory of toda like integrable systems using the gauss borel factorization of a cantero moral velazquez moment matrix that we construct in terms of a complex quasi definite measure supported on the unit circle the factorization of the moment matrix leads to orthogonal laurent polynomials on the unit circle and the corresponding second kind functions we obtain jacobi operators 5 term recursion relations christoffel darboux kernels and corresponding christoffel darboux formulas from this point of view in a completely algebraic way we generalize the cantero moral velazquez sequence of laurent monomials recursion relations christoffel darboux kernels and corresponding christoffel darboux formulas in this extended context we introduce continuous deformations of the moment matrix and we show how they induce a time dependent orthogonality problem related to a toda type integrable system which is connected with the well known toeplitz lattice we obtain the lax and zakharov shabat equations using the classical integrability theory tools we explicitly derive the dynamical system associated with the coefficients of the orthogonal laurent polynomials and we compare it with the classical toeplitz lattice dynamical system for the verblunsky coefficients of szeg polynomials for a positive measure discrete flows are introduced and related to darboux transformations finally we obtain the representation of the orthogonal laurent polynomials and their second kind functions using the formalism of miwa shifts in terms of functions and the subsequent bilinear equations

matrix orthogonal laurent polynomials on the unit circle and toda type integrable systems matrix orthogonal laurent polynomials in the unit circle and the theory of toda like integrable systems are connected using the gauss borel factorization of two left and a right cantero morales velazquez block moment matrices which are constructed using a quasi definite matrix measure a block gauss borel factorization problem of these moment matrices leads to two sets of biorthogonal matrix orthogonal laurent polynomials and matrix szeg polynomials which can be expressed in terms of schur complements of bordered truncations of the block moment matrix the corresponding block extension of the christoffel darboux theory is derived deformations of the quasidefinite matrix measure leading to integrable systems of toda type are studied the integrable theory is given in this matrix scenario wave and adjoint wave functions lax and zakharov shabat equations bilinear equations and discrete flows connected with darboux transformations we generalize the integrable flows of the cafasso s matrix extension of the toeplitz lattice for the verblunsky coefficients of szeg polynomials an analysis of the miwa shifts allows for the finding of interesting connections between christoffel darboux kernels and miwa shifts of the matrix orthogonal laurent polynomials

difference and differential equations for deformed laguerre hahn orthogonal polynomials on the unit circle sequences of orthogonal polynomials on the unit circle whose caratheodory function satisfies a riccati type differential equation with polynomial coefficients are studied we deduce discrete lax equations which lead to difference equations for the corresponding sequences of reflection parameters and we analyze the continuous differential equations that arise when deformations through a dependence on a parameter t occur

contraction based stabilisation of nonlinear singularly perturbed systems and application to high gain feedback abstractrecent development of contraction theory based analysis has opened the door for inspecting differential behaviour of singularly perturbed systems in this paper a contraction theory based framework is proposed for stabilisation of singularly perturbed systems the primary objective is to design a feedback controller to achieve bounded tracking error for both standard and non standard singularly perturbed systems this framework provides relaxation over traditional quadratic lyapunov based method as there is no need to satisfy interconnection conditions during controller design algorithm moreover the stability bound does not depend on smallness of singularly perturbed parameter and robust to additive bounded uncertainties combined with high gain scaling the proposed technique is shown to assure contraction of approximate feedback linearisable systems these findings extend the class of nonlinear systems which can be made contracting

technical communique a graph theoretic method to find decentralized fixed modes of lti systems this paper deals with the decentralized pole assignability of interconnected systems by means of linear time invariant lti controllers a simple graph theoretic approach is proposed to identify the distinct decentralized fixed modes dfms of the system i e the unrepeated modes which cannot be moved by means of a lti decentralized controller the state space representation of the system is transformed to the decoupled form using a proper change of coordinates for any unrepeated mode a matrix is then computed which resembles the transfer function matrix of the system at some point in the complex plane a bipartite graph is constructed accordingly in terms of the computed matrix now the problem of verifying if this mode is a dfm of the system reduces to checking if the constructed graph has a complete bipartite subgraph with a certain property the sole restriction of this work is that it is only capable of identifying the distinct dfms of a system however it is axiomatic that most of the modes of the real world systems are normally distinct the primary advantage of the present paper is its simplicity compared to the existing ones which often require evaluating the rank of several matrices

spectral transformations for hermitian toeplitz matrices in this paper we deal with some perturbations of probability measures supported on the unit circle as well as in a more general framework with hermitian linear functionals we focus our attention in the hessenberg matrix associated with the multiplication operator in terms of an orthogonal basis in the linear space of polynomials with complex coefficients the lu and qr factorizations of such a matrix are introduced then the connection between the above mentioned perturbations and such factorizations is presented

discrete time control of continuous systems with approximate decentralized fixed modes in this paper the discrete time control of decentralized continuous time systems which have approximate decentralized fixed modes is studied it is shown that under certain conditions discrete time controllers can improve the overall performance of the decentralized control system when a linear time invariant continuous time controller is ineffective in order to obtain these conditions a quantitative measure for different types of approximate fixed modes in a decentralized system is given in this case it is shown that discrete time zero order hold zoh controllers and in particular that generalized sampled data hold functions gshf can significantly improve the overall performance of the resultant closed loop system the proposed sampled data controller is in fact a linear time varying controller for the continuous time system

rational spectral transformations and orthogonal polynomials abstract we show that generic rational transformations of the stieltjes function with polynomial coefficients st can be presented as a finite superposition of four fundamental elementary transforms christoffel transform ct geronimus transform gt and forward and backward associated transformations a t a t it is shown that the laguerre hahn polynomials lhp on arbitrary nonuniform lattice are covariant with respect to st i e st of a lhp yields another lhp whereas the semi classical polynomials are covariant with respect to a subclass of linear st some applications of these results to the theory of the semi classical polynomials are considered

orthogonal polynomials and quadrature rules on the unit circle associated with perturbations of symmetric measures abstract it was shown recently that given a pair of real sequences c n n 1 d n n 1 with d n n 1 a positive chain sequence we can associate a unique nontrivial probability measure on the unit circle and conversely in this paper we consider the set q c of all nontrivial probability measures for which c n 1 n c with c r we show that every measure q c can be obtained from a perturbation of a symmetric measure on 1 1 moreover the sequence of orthogonal polynomials associated with can be given in terms of a perturbation of symmetric orthogonal polynomials associated with we also prove that every measure in q c is quasi symmetric that is there exists a complex valued function q c z satisfying d z q c z d z and such that q c z 1 when c 0 quadrature rules with quasi symmetric weights are also considered finally some examples of orthogonal polynomials on the unit circle and its associated quasi symmetric nontrivial probability measures are obtained

brief paper control of continuous time lti systems by means of structurally constrained controllers this paper deals with the characterization of the fixed modes of multi channel systems with respect to linear time invariant lti structurally constrained controllers fixed modes can be found numerically for any lti system with respect to any given control structure using a random number generator the existing analytical methods however are not capable of characterizing the fixed modes in the most general case of non strictly proper systems with non block diagonal i e overlapping control structure efficiently the notion of a decentralized overlapping fixed mode dofm is introduced in this paper to address the above problem in the most general case to this end the knowledge of the overlapping control structure is translated into a bipartite graph whose vertices correspond to the input and output vectors of various control channels an efficient technique is applied to the obtained graph to identify the dofms of the system it is to be noted that a system is stabilizable via an appropriate lti decentralized overlapping controller if and only if it does not have any unstable dofm moreover it is shown how those modes which are not dofms can be placed freely in the complex plane using a proper lti decentralized overlapping controller the efficacy of this work is demonstrated through an example

moment modification multipeakons and nonisospectral generalizations abstract firstly a formal correspondence is established between the camassa holm ch equation and a two component modified ch or called sqq equation according to the method of moment modification for multipeakon formulae secondly based on the generalized nonisospectral ch equation in chang et al 2014 14 and the interlacing multipeakons of the two component modified ch equation in chang et al 2016 15 we propose a new generalized two component modified ch equation with two parameters which possesses a nonisospectral lax pair the proposed equation still admits multipeakon solutions of explicit and closed form sufficient conditions for global existence of solutions are given and two concrete examples with certain interesting phenomenon are presented last of all as a by product a generalized nonisospectral modified ch equation is deduced together with its lax pair

dynamic surface control for a class of nonlinear systems a method is proposed for designing controllers with arbitrarily small tracking error for uncertain mismatched nonlinear systems in the strict feedback form this method is another synthetic input technique similar to backstepping and multiple surface control methods but with an important addition spl tau 1 low pass filters are included in the design where spl tau is the relative degree of the output to be controlled it is shown that these low pass filters allow a design where the model is not differentiated thus ending the complexity arising due to the explosion of terms that has made other methods difficult to implement in practice the backstepping approach while suffering from the problem of explosion of terms guarantees boundedness of tracking errors globally however the proposed approach while being simpler to implement can only guarantee boundedness of tracking error semiglobally when the nonlinearities in the system are non lipschitz

perturbations on the antidiagonals of hankel matrices given a strongly regular hankel matrix and its associated sequence of moments which defines a quasi definite moment linear functional we study the perturbation of a fixed moment i e a perturbation of one antidiagonal of the hankel matrix we define a linear functional whose action results in such a perturbation and establish necessary and sufficient conditions in order to preserve the quasi definite character a relation between the corresponding sequences of orthogonal polynomials is obtained as well as the asymptotic behavior of their zeros we also study the invariance of the laguerre hahn class of linear functionals under such perturbation and determine its relation with the so called canonical linear spectral transformations

pade approximants and complex high order toda lattices tridiagonal operators with complex coefficients are considered the correspondence between dynamics of high order toda equations for the coefficients of the operator and its resolvent function is established it gives a method to solve an inverse problem integration of high order toda equations with complex initial data based on pade approximants and continued fractions for the resolvent function

dynamic surface control via singular perturbation analysis this note contributes to the technical nature of dynamic surface control dsc based on a class of strict feedback nonlinear systems the dsc technique prevents the complexity problem in integrator backstepping control ibc yet the stability results obtained by existing dscs are conservative and consequently cannot fully reveal the technical nature of dsc by the exploitation of the singular perturbation theory several novel features of dsc are revealed as follows 1 semiglobal practical exponential stability can be guaranteed only by a suitably small filter parameter 2 steady state tracking accuracy does not rely on high control gains 3 the performance of ibc can be recovered via the decrease of the filter parameter these features are not only significant for understanding the technical nature of dsc but also useful for establishing an efficient strategy of parameter selection and system debugging simulation results have verified correctness of the theoretical result

on differential equations for orthogonal polynomials on the unit circle in this paper we characterize sequences of orthogonal polynomials on the unit circle whose corresponding caratheodory function satisfies a riccati differential equation with polynomial coefficients in terms of second order matrix differential equations in the semi classical case a characterization in terms of second order linear differential equations with polynomial coefficients is deduced

szegő difference equations transfer matrices and orthogonal polynomials on the unit circle we develop the theory of orthogonal polynomials on the unit circle based on the szeg recurrence relations written in matrix form the orthogonality measure and c function arise in exactly the same way as weyl s function in the weyl approach to second order linear differential equations on the half line the main object under consideration is the transfer matrix which is a key ingredient in the modern theory of one dimensional schrodinger operators discrete and continuous and the notion of subordinacy from the gilbert pearson theory we study the relations between transfer matrices and the structure of orthogonality measures the theory is illustrated by the szeg equations with reflection coefficients having bounded variation

on the full kostant toda system and the discrete korteweg de vries equations abstract the relation between the solutions of the full kostant toda lattice and the discrete korteweg de vries equation is analyzed a method for constructing solutions of these systems is given as a consequence of the matricial interpretation of this method the transform of darboux is extended for general hessenberg banded matrices

matrix toda and volterra lattices abstract we consider matrix toda and volterra lattice equations and their relation with matrix biorthogonal polynomials from that relation we give a method for constructing a new solution of these systems from another given one an illustrative example is presented

brief paper adaptive dynamic surface control for linear multivariable systems in this paper an output feedback adaptive control is presented for linear time invariant multivariable plants by using the dynamic surface control technique it is shown that the explosion of complexity problem in multivariable backstepping design can be eliminated the proposed scheme has the following features 1 the l performance of the system s tracking error can be guaranteed 2 it has least number of updated parameters in comparison with other multivariable adaptive schemes and 3 the adaptive law is necessary only at the first design step which significantly reduces the design procedure simulation results are presented to demonstrate the effectiveness of the proposed scheme

sieved para orthogonal polynomials on the unit circle abstract sieved orthogonal polynomials on the unit circle were introduced independently by ismail and li 1992 15 and marcellan and sansigre 1991 19 we look at the para orthogonal polynomials chain sequences and quadrature formulas that follow from the kernel polynomials of sieved orthogonal polynomials on the unit circle

analogs of the m function in the theory of orthogonal polynomials on the unit circle we show that the multitude of applications of the weyl titchmarsh m function leads to a multitude of different functions in the theory of orthogonal polynomials on the unit circle that serve as analogs of the m function

distributional equation for laguerre hahn functionals on the unit circle let u be a hermitian linear functional defined in the linear space of laurent polynomials and f its corresponding caratheodory function we establish the equivalence between a riccati differential equation with polynomial coefficients for f zaf bf 2 cf d and a distributional equation for u d au b u 2 c u h l where l is the lebesgue functional and the polynomials b c h are defined in terms of the polynomials a b c d

special solutions of the toda chain and combinatorial numbers we classify all solutions of the restricted toda chain from the ansatz that all moments are expressed in terms of polynomials of some variable we show that each such solution corresponds to the sheffer class orthogonal polynomials it is shown that corresponding hankel determinants are related to some well known combinatorial numbers

elliptic solutions of the restricted toda chain lame polynomials and generalization of the elliptic stieltjes polynomials we construct new families of elliptic solutions of the restricted toda chain the main tool is a special so called stieltjes ansatz for the moments of corresponding orthogonal polynomials we show that the moments thus obtained are related to three types of lam polynomials the corresponding orthogonal polynomials can be considered as a generalization of the stieltjes carlitz elliptic polynomials

on polynomials associated with an uvarov modification of a quartic potential freud like weight in this contribution we consider sequences of monic polynomials orthogonal with respect to the standard freud like inner product involving a quartic potential p q r p x q x e x 4 2 t x 2 d x m p 0 q 0 we analyze some properties of these polynomials such as the ladder operators and the holonomic equation that they satisfy and as an application we give an electrostatic interpretation of their zero distribution in terms of a logarithmic potential interaction under the action of an external field it is also shown that the coefficients of their three term recurrence relation satisfy a nonlinear difference string equation finally an equation of motion for their zeros in terms of their dependence on t is given

perturbations on the subdiagonals of toeplitz matrices let l be an hermitian linear functional defined on the linear space of laurent polynomials it is very well known that the gram matrix of the associated bilinear functional in the linear space of polynomials is a toeplitz matrix in this contribution we analyze some linear spectral transforms of l such that the corresponding toeplitz matrix is the result of the addition of a constant in a subdiagonal of the initial toeplitz matrix we focus our attention in the analysis of the quasi definite character of the perturbed linear functional as well as in the explicit expressions of the new monic orthogonal polynomial sequence in terms of the first one