内积空间中Witt定理的推广

在特征不是2的正交空间中,相关文献给出了Witt定理.华罗庚把它推广到体上的一些内积空间.把域上内积空间中的Witt定理推广到奇异内积空间,并给出相应的证明.     

基于混沌表示的广义Fock空间

混沌表示是白噪声分析的关键.考虑目前的基于广义Fock空间的两种混沌分解所依赖的n粒子空间的内积,本文得到了这两种n粒子空间的内积以及两种广义Fock空间的关系.     

Multilinearity partitions of characters of embedded groups *

We show that a well-known polarization formula for Hermitian inner products on complex vector spaces generalizes to the case of inner products on Clifford modules. This observation allows us to conclude that norm-preserving linear maps of Clifford modules necessarily preserve the inner product. These results hold for modules over the quaternious as a special case.     

A polarization formula for clifford modules

We show that a well-known polarization formula for Hermitian inner products on complex vector spaces generalizes to the case of inner products on Clifford modules. This observation allows us to conclude that norm-preserving linear maps of Clifford modules necessarily preserve the inner product. These results hold for modules over the quaternious as a special case.     

Group averaging for de Sitter free fields in terms of hyperspherical functions

We study the convergence of inner products of free fields over the homogeneous spaces of the de Sitter group and show that the convergence of inner products in the case of N-particle states is defined by the asymptotic behavior of hypergeometric functions. We calculate the inner product for two-particle states on the four-dimensional hyperboloid in detail.     

On the norm of the product of linear functionals

Real inner product spaces are characterized by the points at which the homogeneous 2-polynomials that are products of equal-norm linear functionals attain their norm.

     

A note on uniform approximation by the indestructibles

We modify an idea in an earlier paper to enlarge the collection of inner functions that are known to be in the uniform closure of the indestructible Blaschke products.     

Self‐adjoint Sturm–Liouville problems with an infinite number of boundary conditions

We study Sturm–Liouville (SL) problems on an infinite number of intervals, adjacent endpoints are linked by means of boundary conditions, and characterize the conditions which determine self‐adjoint operators in a Hilbert space which is the direct sum of the spaces for each interval. These conditions can be regular or singular, separated or coupled. Furthermore, the inner products of the summand spaces may be multiples of the usual inner products with different spaces having different multiples. We also extend the GKN Theorem to cover the infinite number of intervals theory with modified inner products and discuss the connection between our characterization and the classical one with the usual inner products. Our results include the finite number of intervals case.     

Weighted inner products of derivatives of L2-holomorphic functions on the unit ball

In this paper, we give an algorithmic method of constructing inner product formulas which contain weighted inner products of holomorphic functions on the unit ball. This result covers all inner product formulas which have been proved before. As an application, we prove Zhu’s characterization theorem by an elementary method. Finally, by using one-to-one correspondence between inner product formulas and lattices with circles, we prove all inner product formulas again without any complicated computation.     

A note on the Geronimus transformation and Sobolev orthogonal polynomials

In this note we recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms. We also show that the double Geronimus transformations lead to non-diagonal Sobolev type inner products.     

On the convergence of row-modification algorithm for matrix projections

This paper proposes an algorithm for matrix minimum-distance projection, with respect to a metric induced from an inner product that is the sum of inner products of column vectors, onto the collection of all matrices with their rows restricted in closed convex sets. This algorithm produces a sequence of matrices by modifying a matrix row by row, over and over again. It is shown that the sequence is convergent, and it converges to the desired projection. The implementation of the algorithm for multivariate isotonic regressions and numerical examples are also presented in the paper.     

Ordered OLPS and CF Nth numerators

Definitions, theorems and examples are established for a general model of Laurent polynomial spaces and ordered orthogonal Laurent polynomial sequences, ordered with respect to ordered bases and orthogonal with respect to inner products ·=L°⊙ decomposed into transition functional ⊙ and strong moment functional, or, more generally, sample functional L couplings. Under this formulation that is shown to subsume those in the existing literature, new fundamental results are produced, including necessary and sufficient conditions for ordered OLPS to be sequences of nth numerators of continued fractions, in contrast to the classical result concerning nth denominators which is shown to hold only in special cases.     

IA-Automorphisms of Metabelian Products of Two Abelian Groups

For metabelian products of two Abelian groups with torsion, IA-automorphisms that are not inner and hence are not induced by any automorphisms of the free products of the same Abelian groups are constructed.     

Minimax problem of determining the tape tension during winding on a compliant bobbin

The object of this report is to analyze the modes in which the tension on the inner turns drops when a tape or a thread are wound on a compliant bobbin as, for example, during processing of glass-plastic products. It is established here under what conditions one cannot possibly ensure a uniform residual tension in all turns upon completion of the winding; for this case, then, the optimum mode of tension change during winding is sought, so that the tension drop in the inner turns will be minimum.     

Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces I: algorithms

In this paper, we study theoretically the determination and evaluation of polynomials that are orthogonal with respect to a general discrete Sobolev inner product, that is, an ordinary inner product on the real line plus a finite sum of atomic inner products involving a finite number of derivatives. This Sobolev inner product has the property that the orthogonal polynomials with respect to it satisfy a linear recurrence relation of fixed order. We provide a complete set of formulas to compute the coefficients of this recurrence. Besides, we study the determination of the Fourier–Sobolev coefficients of a finite approximation of a function and the numerical evaluation of the resulting finite series at a general point.     

关于概率内积空间定义的平凡性

研究了分布函数拟逆的性质,进而利用这些性质,讨论了概率内积空间中半内积族之间的关系,并证明了几种定义下的概率内积空间等同于通常的内积空间.     

A Product Theorem for Intersection Families

We will consider a certain kind of intersection family: a family of vectors over a field of finite characteristic q, such that the generalized inner products of every q or fewer vectors take on prescribed values. For certain values of the parameters, these values distinguish the generalized inner product of any q distinct vectors, from that of any q vectors in which some vector is repeated.We will represent such an intersection family by its incidence matrix, and show that the matrix product of two such matrices is itself an intersection family of the type under consideration. If the factor families distinguish between generalized inner products of q vectors with or without repetition, then so does the product family.     

Inner functions in weak Besov spaces

It is shown that inner functions in weak Besov spaces are precisely the exponential Blaschke products.