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1.
A sequence of continuous linear operators is said to be hypercyclic if there exists a vector , called hypercyclic for , such that {Tnx:n0} is dense. A continuous linear operator, acting on some suitable function space, is PDE-preserving for a given set of convolution operators, when it map every kernel set for these operators invariantly. We establish hypercyclic sequences of PDE-preserving operators on , and study closed infinite-dimensional subspaces of, except for zero, hypercyclic vectors for these sequences.  相似文献   

2.
Let mp be the minimum of the product under the conditions that and . In our previous paper [J. Kaneko, On an extremal problem of Selberg, J. Approx. Theory 142 (2006) 129–137], we showed that the following estimates hold. provided p255. In this note, we prove that the limit of as p→∞ exists and is expressed by the (unique) solution of some simultaneous transcendental equations. By using this expression we obtain numerically.  相似文献   

3.
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   

4.
Wolfgang Rump   《Journal of Algebra》2007,310(2):648-670
We associate a positive real number to any vector space K-category over a field K. Generalizing a result of Nazarova and Roiter, we show that a schurian vector space K-category is representation-finite if and only if is finite and . Such vector space categories are quasilinear, i.e. its indecomposables are simple modules over their endomorphism ring. Recently, Nazarova and Roiter introduced the concept of -faithful poset in order to clarify the structure of critical posets. Their conjecture on the precise form of -faithful posets was established by Zeldich. We generalize these results and characterize -faithful quasilinear vector space K-categories in terms of a class of hereditary algebras Hρ(D) parametrized by a skew-field D and a rational number ρ1.  相似文献   

5.
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   

6.
Let X denote a (real) Banach space and V an n-dimensional subspace. We denote by the space of all bounded linear operators from X into V; let be the set of all projections in . For a given , we denote by the set of operators such that PSS. When , we characterize those for which P is minimal. This characterization is then utilized in several applications and examples.  相似文献   

7.
We describe an algorithm for constructing a Lagrange interpolation pair based on C1 cubic splines defined on tetrahedral partitions. In particular, given a set of points , we construct a set P containing and a spline space based on a tetrahedral partition whose set of vertices include such that interpolation at the points of P is well-defined and unique. Earlier results are extended in two ways: (1) here we allow arbitrary sets , and (2) the method provides optimal approximation order of smooth functions.  相似文献   

8.
Dan Yasaki   《Journal of Algebra》2009,322(11):4132
Let ζ be a primitive fifth root of unity and let F be the cyclotomic field . Let be the ring of integers. We compute the Voronoï polyhedron of binary Hermitian forms over F and classify -conjugacy classes of perfect forms. The combinatorial data of this polyhedron can be used to compute the cohomology of the arithmetic group and Hecke eigenforms.  相似文献   

9.
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   

10.
The well-known density theorem for one-dimensional Gabor systems of the form , where , states that a necessary and sufficient condition for the existence of such a system whose linear span is dense in , or which forms a frame for , is that the density condition is satisfied. The main goal of this paper is to study the analogous problem for Gabor systems for which the window function g vanishes outside a periodic set which is -shift invariant. We obtain measure-theoretic conditions that are necessary and sufficient for the existence of a window g such that the linear span of the corresponding Gabor system is dense in L2(S). Moreover, we show that if this density condition holds, there exists, in fact, a measurable set with the property that the Gabor system associated with the same parameters a,b and the window g=χE, forms a tight frame for L2(S).  相似文献   

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