denote the zeros of nth m-orthogonal polynomial for a generalized Jacobi weight
This note proves . The gap left over , is filled.  相似文献   

10.
On a max-type and a min-type difference equation     
E.M. Elsayed  Bratislav D. Iri anin 《Applied mathematics and computation》2009,215(2):608-614
This note shows that every positive solution to the following third order non–autonomous max-type difference equation
when is a three-periodic sequence of positive numbers, is periodic with period three. The same result was proved for the following min-type difference equation
  相似文献   

11.
On the sampling and recovery of bandlimited functions via scattered translates of the Gaussian     
Th. Schlumprecht  N. Sivakumar   《Journal of Approximation Theory》2009,159(1):128
Let λ be a positive number, and let be a fixed Riesz-basis sequence, namely, (xj) is strictly increasing, and the set of functions is a Riesz basis (i.e., unconditional basis) for L2[−π,π]. Given a function whose Fourier transform is zero almost everywhere outside the interval [−π,π], there is a unique sequence in , depending on λ and f, such that the function
is continuous and square integrable on (−,), and satisfies the interpolatory conditions Iλ(f)(xj)=f(xj), . It is shown that Iλ(f)converges to f in , and also uniformly on , as λ→0+. In addition, the fundamental functions for the univariate interpolation process are defined, and some of their basic properties, including their exponential decay for large argument, are established. It is further shown that the associated interpolation operators are bounded on for every p[1,].  相似文献   

12.
Stationary twists and energy minimizers on a space of measure preserving maps     
Ali Taheri   《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5672-5687
Let be a bounded Lipschitz domain, a suitably quasiconvex integrand and consider the energy functional
over the space of measure preserving maps
In this paper we discuss the question of existence of multiple strong local minimizers for over . Moreover, motivated by their significance in topology and the study of mapping class groups, we consider a class of maps, referred to as twists, and examine them in connection with the corresponding Euler–Lagrange equations and investigate various qualitative properties of the resulting solutions, the stationary twists. Particular attention is paid to the special case of the so-called p-Dirichlet energy, i.e., when .  相似文献   

13.
Vector refinement equations with infinitely supported masks     
Song Li  Jianbin Yang 《Journal of Approximation Theory》2007,148(2):158-176
In this paper we investigate the L2-solutions of vector refinement equations with exponentially decaying masks and a general dilation matrix. A vector refinement equation with a general dilation matrix and exponentially decaying masks is of the form
where the vector of functions φ=(φ1,…,φr)T is in is an exponentially decaying sequence of r×r matrices called refinement mask and M is an s×s integer matrix such that limn→∞M-n=0. Associated with the mask a and dilation matrix M is a linear operator Qa on given by
The iterative scheme is called vector subdivision scheme or vector cascade algorithm. The purpose of this paper is to provide a necessary and sufficient condition to guarantee the sequence to converge in L2-norm. As an application, we also characterize biorthogonal multiple refinable functions, which extends some main results in [B. Han, R.Q. Jia, Characterization of Riesz bases of wavelets generated from multiresolution analysis, Appl. Comput. Harmon. Anal., to appear] and [R.Q. Jia, Convergence of vector subdivision schemes and construction of biorthogonal multiple wavelets, Advances in Wavelet (Hong Kong, 1997), Springer, Singapore, 1998, pp. 199–227] to the general setting.  相似文献   

14.
Two canonical passive state/signal shift realizations of passive discrete time behaviors     
Damir Z. Arov  Olof J. Staffans   《Journal of Functional Analysis》2009,257(8):2573-2634
A discrete time invariant linear state/signal system Σ with a Hilbert state space and a Kren signal space has trajectories (x(),w()) that are solutions of the equation , where F is a bounded linear operator from into with a closed domain whose projection onto is all of . This system is passive if the graph of F is a maximal nonnegative subspace of the Kren space . The future behavior of a passive system Σ is the set of all signal components w() of trajectories (x(),w()) of Σ on with x(0)=0 and . This is always a maximal nonnegative shift-invariant subspace of the Kren space , i.e., the space endowed with the indefinite inner product inherited from . Subspaces of with this property are called passive future behaviors. In this work we study passive state/signal systems and passive behaviors (future, full, and past). In particular, we define and study the input and output maps of a passive state/signal system, and the past/future map of a passive behavior. We then turn to the inverse problem, and construct two passive state/signal realizations of a given passive future behavior , one of which is observable and backward conservative, and the other controllable and forward conservative. Both of these are canonical in the sense that they are uniquely determined by the given data , in contrast earlier realizations that depend not only on , but also on some arbitrarily chosen fundamental decomposition of the signal space . From our canonical realizations we are able to recover the two standard de Branges–Rovnyak input/state/output shift realizations of a given operator-valued Schur function in the unit disk.  相似文献   

15.
On solvability of boundary value problems for higher order nonlinear hyperbolic equations     
Ivan Kiguradze  Tariel Kiguradze   《Nonlinear Analysis: Theory, Methods & Applications》2008,69(7):1914-1933
In the rectangle Ω=[0,a]×[0,b] for the nonlinear hyperbolic equation
the boundary value problems of the type
are considered, where and are linear bounded functionals.Sufficient conditions of solvability and unique solvability of the general problem and its particular cases (Nicoletti type, Dirichlet, Lidstone and Periodic problems) are established.  相似文献   

16.
Christoffel-type functions for -orthogonal polynomials for Freud weights     
Ying Guang Shi   《Journal of Approximation Theory》2007,144(2):247-259
This paper gives upper and lower bounds of the Christoffel-type functions , for the m-orthogonal polynomials for a Freud weight W=e-Q, which are given as follows. Let an=an(Q) be the nth Mhaskar–Rahmanov–Saff number, φn(x)=max{n-2/3,1-|x|/an}, and d>0. Assume that QC(R) is even, , and for some A,B>1
Then for xR
and for |x|an(1+dn-2/3)
  相似文献   

17.
Nonnegative solutions of the characteristic initial value problem for linear partial functional–differential equations of hyperbolic type     
A. Lomtatidze  S. Mukhigulashvili  J. &#x;remr 《Mathematical and Computer Modelling》2008,47(11-12):1292-1313
On the rectangle , the problem on the existence and uniqueness of a nonnegative solution of the characteristic initial value problem for the equation
is considered, where is a linear bounded operator and .  相似文献   

18.
n-Star modules over ring extensions     
Jiaqun Wei   《Journal of Algebra》2007,310(2):903-916
We give conditions under which an n-star module extends to an n-star module, or an n-tilting module, over a ring extension R of A. In case that R is a split extension of A by Q, we obtain that is a 1-tilting module (respectively, a 1-star module) if and only if is a 1-tilting module (respectively, a 1-star module) and generates both and (respectively, generates ), where is an injective cogenerator in the category of all left A-modules. These extend results in [I. Assem, N. Marmaridis, Tilting modules over split-by-nilpotent extensions, Comm. Algebra 26 (1998) 1547–1555; K.R. Fuller, *-Modules over ring extensions, Comm. Algebra 25 (1997) 2839–2860] by removing the restrictions on R and Q.  相似文献   

19.
Gagliardo–Nirenberg inequalities in regular Orlicz spaces involving nonlinear expressions     
Agnieszka Ka&#x;amajska  Miroslav Krbec 《Journal of Mathematical Analysis and Applications》2010,362(2):460-470
We consider a triple of N-functions (M,H,J) that satisfy the Δ-condition, and suppose that an additive variant of interpolation inequality holds
where , is an arbitrary set invariant with respect to external and internal dilations. We show that the above inequality implies its certain nonlinear variant involving the expressions and . Various generalizations of this inequality to the more general class of N-functions, measures and to higher order derivatives are also discussed and the examples are presented.  相似文献   

20.
A spectral equivalence for Jacobi matrices     
E. Ryckman   《Journal of Approximation Theory》2007,146(2):252-266
We use the classical results of Baxter and Golinskii–Ibragimov to prove a new spectral equivalence for Jacobi matrices on . In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences and find necessary and sufficient conditions on the spectral measure such that and lie in or for s1.  相似文献   

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1.
The zero sets of (D+a)ng(t) with in the (t,a)-plane are investigated for and .The results are used to determine entire interpolations to functions , which give representations for the best approximation and best one-sided approximation from the class of functions of exponential type η>0 to .  相似文献   

2.
Let be a bounded domain such that 0Ω. Denote by , the set of all complex polynomials of degree at most n. Let
where . We relate the maximal polynomial range
to the geometry of Ω.  相似文献   

3.
Let p be a trigonometric polynomial, non-negative on the unit circle . We say that a measure σ on belongs to the polynomial Szegő class, if , σs is singular, and
For the associated orthogonal polynomials {n}, we obtain pointwise asymptotics inside the unit disc . Then we show that these asymptotics hold in L2-sense on the unit circle. As a corollary, we get an existence of certain modified wave operators.  相似文献   

4.
We relate asymptotics of Jacobi parameters to asymptotics of the spectral weights near the edges. Typical of our results is that for an≡1, bn=−Cnβ (), one has on (−2,2), and near x=2, where
  相似文献   

5.
A family of orthonormal polynomials on the unit ball Bd of with respect to the inner product
where Δ is the Laplace operator, is constructed explicitly.  相似文献   

6.
Let be the usual Sobolev class of functions on the unit ball in , and be the subclass of all radial functions in . We show that for the classes and , the orders of best approximation by polynomials in coincide. We also obtain exact orders of best approximation in of the classes by ridge functions and, as an immediate consequence, we obtain the same orders in for the usual Sobolev classes .  相似文献   

7.
For a graph property , the edit distance of a graph G from , denoted , is the minimum number of edge modifications (additions or deletions) one needs to apply to G in order to turn it into a graph satisfying . What is the largest possible edit distance of a graph on n vertices from ? Denote this distance by .A graph property is hereditary if it is closed under removal of vertices. In a previous work, the authors show that for any hereditary property, a random graph essentially achieves the maximal distance from , proving: with high probability. The proof implicitly asserts the existence of such , but it does not supply a general tool for determining its value or the edit distance.In this paper, we determine the values of and for some subfamilies of hereditary properties including sparse hereditary properties, complement invariant properties, (r,s)-colorability and more. We provide methods for analyzing the maximum edit distance from the graph properties of being induced H-free for some graphs H, and use it to show that in some natural cases G(n,1/2) is not the furthest graph. Throughout the paper, the various tools let us deduce the asymptotic maximum edit distance from some well studied hereditary graph properties, such as being Perfect, Chordal, Interval, Permutation, Claw-Free, Cograph and more. We also determine the edit distance of G(n,1/2) from any hereditary property, and investigate the behavior of as a function of p.The proofs combine several tools in Extremal Graph Theory, including strengthened versions of the Szemerédi Regularity Lemma, Ramsey Theory and properties of random graphs.  相似文献   

8.
V.V. Bavula  T.H. Lenagan   《Journal of Algebra》2008,320(12):4132-4155
Let K be an arbitrary field of characteristic zero, Pn:=K[x1,…,xn] be a polynomial algebra, and , for n2. Let σAutK(Pn) be given by
It is proved that the algebra of invariants, , is a polynomial algebra in n−1 variables which is generated by quadratic and cubic (free) generators that are given explicitly.Let σAutK(Pn) be given by
It is well known that the algebra of invariants, , is finitely generated (theorem of Weitzenböck [R. Weitzenböck, Über die invarianten Gruppen, Acta Math. 58 (1932) 453–494]), has transcendence degree n−1, and that one can give an explicit transcendence basis in which the elements have degrees 1,2,3,…,n−1. However, it is an old open problem to find explicit generators for Fn. We find an explicit vector space basis for the quadratic invariants, and prove that the algebra of invariants is a polynomial algebra over in n−2 variables which is generated by quadratic and cubic (free) generators that are given explicitly.The coefficients of these quadratic and cubic invariants throw light on the ‘unpredictable combinatorics’ of invariants of affine automorphisms and of SL2-invariants.  相似文献   

9.
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