automorphisms of the fine grading of sl n c associated with the generalized pauli matrices we consider the grading of sl n c by the group n of generalized pauli matrices the grading decomposes the lie algebra into n2 1 one dimensional subspaces in the article we demonstrate that the normalizer of grading decomposition of sl n c in n is the group sl 2 zn where zn is the cyclic group of order n as an example we consider sl 3 c graded by 3 and all contractions preserving that grading we show that the set of 48 quadratic equations for grading parameters splits into just two orbits of the normalizer of the grading in 3

on lie gradings ii abstract to obtain fine gradings of gl n c it is necessary to study maximal abelian subgroups mad subgroups of diagonizable automorphisms in a ut gl n c we described two finite sets h n and k n such that each mad subgroup consisting only from inner automorphisms is conjugated to some element of h n and each mad subgroup containing at least one outer automorphism is conjugated to some element of k n using these results concerning k n we then easily find all mad subgroups in a ut o n c for n 8 and in a ut sp 2n c

the weyl group of the fine grading of sl n c associated with tensor product of generalized pauli matrices we consider the fine grading of sl n c induced by tensor product of generalized pauli matrices in the paper regard pgl n c as the inner automorphism group of sl n c based on the classification of maximal abelian subgroups of pgl n c consisting of diagonalizable automorphisms by havlicek et al we prove that any such subgroup k of pgl n c is a symplectic abelian group and its weyl group which describes the symmetry of the fine grading induced by the action of k is just the isometry group of the symplectic abelian group k for a finite symplectic abelian group it is also proved that its isometry group is always generated by the transvections contained in it

norm and essential norm of composition followed by differentiation from α bloch spaces to hμ abstract this note calculates the norm of composition followed by differentiation operator from the bloch and the little bloch space to the weighted space h on the unit disk and gives an upper and a lower bound for the essential norm of the operator from the bloch space b 0 to h

on an integral type operator from logarithmic bloch type and mixed norm spaces to bloch type spaces abstract this paper studies the boundedness and compactness of the following integral type operator recently introduced by this author p g f z 0 1 f t z g t z d t t z b where is a holomorphic self map of the unit ball b in c n and g is a holomorphic function on b such that g 0 0 from logarithmic bloch type and mixed norm spaces to bloch type spaces

fine gradings on simple classical lie algebras abstract the fine abelian group gradings on the simple classical lie algebras including d 4 over algebraically closed fields of characteristic 0 are determined up to equivalence this is achieved by assigning certain invariant to such gradings that involve central graded division algebras and suitable sesquilinear forms on free modules over them

special and pure gradings of lie algebras 136 w h hesselink m f p since h is strict the mapf is uniquely determined by the gradings h and h conversely the grading h is determined by h and f if n is a subgroup of m and m m n and f is the quotient map then h is called the quotient grading h h n see 2 8 for an example strict gradings h and are called equivalent if they dominate each other they are called conjugate if there is an automorphism g of l such that h is equivalent to the grading gh ghm m m the automorphism group a h of a strict grading h of l is defined to consist of the automorphisms g of l such that gh is equivalent to h let a h be the image of a h in the automor phism group gl m of m in 3 9 we prove proposition a a h is a finite group b let l be semisimple then a h is finite if and only if h is special 1 4 let l be a semisimple lie algebra over k of rank 1 if h is a pure grading of l its graduation group m is an lf2 space of rank r with 1 r 1 cf 4 1 assume that l has a split caftan subalgebra c let cg l be the root space decomposition of l let 9 be the root system and let q be the lattice spanned by 9 in the dual c of c let w be the weyl group a grading h is called c pure if cch with s 0 since 2s 0 we have the quotient grading h h o s with the graduation group m m o s as c cho there is a unique homomorphism f q m such that l h i if a b since h is strict f is surjective the kernel of f is called the com plementary lattice e of h since m is an ifz space we have 2qce conversely we have

more non semigroup lie gradings this note is devoted to the construction of two very easy examples of respective dimensions 4 and 6 of graded lie algebras whose grading is not given by a semigroup the latter one being a semisimple algebra it is shown that 4 is the minimal possible dimension for such graded lie algebras

fine grading of sl p2 c generated by tensor product of generalized pauli matrices and its symmetries study of the normalizer of the mad group corresponding to a fine grading offers the most important tool for describing symmetries in the system of nonlinear equations connected with contraction of a lie algebra one fine grading that is always present in any lie algebra sl n c is the pauli grading the mad group corresponding to it is generated by generalized pauli matrices for such mad group we already know its normalizer its quotient group is isomorphic to the lie group sl 2 zn z2 in this paper we deal with a more complicated situation namely that the fine grading of sl p2 c is given by a tensor product of the pauli matrices of the same order p p being a prime we describe the normalizer of the corresponding mad group and we show that its quotient group is isomorphic to sp 4 fp z2 where fp is the finite field with p elements

products of composition and differentiation operators from zygmund spaces to bloch spaces and bers spaces abstract the boundedness and compactness of the products of differentiation and composition operators from zygmund spaces to bloch spaces and bers spaces are discussed in this paper

weighted differentiation composition operators from h and bloch spaces to nth weighted type spaces on the unit disk we characterize the boundedness and compactness of weighted differentiation composition operators from the space of bounded analytic functions the bloch space and the little bloch space to nth weighted type spaces on the unit disk

essential norm of generalized weighted composition operators on bloch type spaces in this paper we give some estimates of the essential norm for generalized weighted composition operators on bloch type spaces moreover we give a new characterization for the boundedness and compactness of the generalized weighted composition operator on bloch type spaces

an efficient iterative algorithm for designing optimal recursive digital filters a new iterative algorithm is presented for the efficient design of unconstrained and constrained infinite impulse response iir digital filters both in the unconstrained and constrained cases the numerator and denominator of the filter transfer function are designed iteratively by recourse to the remez algorithm and to appropriate design parameters and criteria at each iteration this makes it possible for the algorithm to be implemented by means of a short main program which uses at each iteration the finite impulse response fir filter design algorithm of mcclellan et al as a subroutine as a consequence the entire design procedure proves to be very efficient the approach taken also permits the filter to be designed with a desired passband to stopband ripple ratio typically the design algorithm converges to the optimal solution within a few iterations several examples are given to illustrate the procedure the filter design computer program is provided in the appendix

a class of efficient recursive quadrature mirror filters for subband coding a class of recursive quadrature mirror filters qmfs of the form h z n z d z sup 2 is proposed for subband coding these filters can be efficiently designed with the iterative remez exchange algorithm simple modifications are made to the pei see ieee trans circuits syst vol cas 36 no 2 p 311 1989 liang mcclellan and parks computer program for designing these recursive qmf filters efficiently the resulting filters totally eliminate the aliasing terms and can achieve almost perfect magnitude reconstruction with 131 5 db distortion a design example is presented to show the effectiveness of this approach

new estimates of essential norms of weighted composition operators between bloch type spaces abstract we give estimates of the essential norms of the weighted composition operators u c between different bloch type spaces in terms of the n th power of we also give similar characterizations for boundedness and compactness of u c between different bloch type spaces

weighted differentiation composition operators from mixed norm spaces to weighted type spaces motivated by the recent paper x zhu products of differentiation composition and multiplication from bergman type spaces to bers spaces integral transform spec funct 18 3 2007 223 231 we study the boundedness and compactness of the weighted differentiation composition operator d f u n f z u z f n f z where u is a holomorphic function on the unit disk d f is a holomorphic self map of d and email protected n 0 from the mixed norm space h p q f where p q 0 and f is normal to the weighted type space h m or the little weighted type space h m 0 for the case of the weighted bergman space a a p p 1 some bounds for the essential norm of the operator are also given

generalized digital butterworth filter design this correspondence introduces a new class of infinite impulse response iir digital filters that unifies the classical digital butterworth filter and the well known maximally flat fir filter new closed form expressions are provided and a straightforward design technique is described the new iir digital filters have more zeros than poles away from the origin and their monotonic square magnitude frequency responses are maximally flat at spl omega 0 and at spl omega spl pi another result of the correspondence is that for a specified cutoff frequency and a specified number of zeros there is only one valid way in which to split the zeros between z 1 and the passband this technique also permits continuous variation of the cutoff frequency iir filters having more zeros than poles are of interest because often to obtain a good tradeoff between performance and implementation complexity just a few poles are best

weighted composition operators from zygmund spaces into bloch spaces abstract let be an analytic self map and u be a fixed analytic function on the open unit disk d in the complex plane c the weighted composition operator is defined by uc f z u z f z z d f h d this paper studies the boundedness and compactness of weighted composition operators from zygmund spaces into bloch spaces

design of finite impulse response digital filters with nonlinear phase response most of the existing literature on fir digital filters is concerned with linear phase lp filters however several papers have appeared on the subject of nonlinear phase nlp filters mainly proposing methods for designing minimum phase filters or approximating a desired phase response in this paper an investigation is made of one such method based upon a selection of zeros from a prototype lp filter it is shown that with respect to minimizing the order of a filter subject to given gain response specifications this is the most efficient method for designing fir filters coefficient quantization error is analyzed for filters generated by this method a practical comparison is given between the resulting filter and the corresponding minimal order lp filter it is shown that while most lp filters can be implemented more efficiently than nlp filters by taking into account the symmetry of their coefficients for filters with very wide passband and for certain special purpose filters such as ccd and those used for filtering a delta modulated or adpcm signal an nlp implementation is usually more efficient in addition an alternate design algorithm is proposed for nlp filters which decreases ripple magnitude the resulting filters while not of minimal order can be efficiently implemented by decomposing the filter into lp stopband and nlp passband sections which is especially attractive for narrow passbands

the symmetries of the fine gradings of sl nk c associated with direct product of pauli groups a grading of a lie algebra is called fine if it could not be further refined for a fine grading of a simple lie algebra we define its weyl group to describe the symmetry of this grading it is already known that the weyl group of the fine grading of sl n c induced by the action of the group n of the generalized pauli matrices of rank n is sl 2 zn where zn is the cyclic group of order n in this paper we consider the fine grading of sl nk c induced by the action of the group of k fold tensor product of the generalized pauli matrices of rank n we prove that its weyl group is sp 2k zn and is generated by transvections therefore this generalizes the previous result