Semi-nonparametric (SNP) models are models where only a part of the model is parametrized, and the non-specified part is an unknown function which is represented by an infinite series expansion. Therefore, SNP models are in essence models with infinitely many parameters. The theoretical foundation of series expansions of functions is Hilbert space theory, in particular the properties of Hilbert...

In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames  are given.  A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is ...

This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels an...

The main goal of this paper is to characterize the Hilbert functions of all (artinian) codimension 4 Gorenstein algebras that have at least two independent relations of degree four. This includes all codimension 4 Gorenstein algebras whose initial relation is of degree at most 3. Our result shows that those Hilbert functions are exactly the so-called SI-sequences starting with (1, 4, h2, h3, .....

This paper contains two main results. The first is a variational representation for the expectation of a measurable function of a Hilbert space valued Brownian motion, when the function is uniformly positive and bounded from above and the Brownian motion has a trace class covariance. This representation is then applied to derive the second main result, which is the large deviation principle for...

We study a natural Hodge module on the Hilbert scheme of four points on affine three-space, which categorifies the Donaldson–Thomas invariant of the Hilbert scheme. We determine the weight filtration on the Hodge module explicitly in terms of intersection cohomology complexes, and compute the E-polynomial of its cohomology. The computations make essential use of a description of the singularity...

G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first generalize the concept of g-frames to Hilbert modules over pro-C*-algebras. Then, we introduce the g-frame operators in such spaces and show that they sha...

We give geometric constructions of families of graded Gorenstein Artin algebras, some of which span a component of the space Gor(T ) parametrizing Gorenstein Artin algebras with a given Hilbert function T . This gives a lot of examples where Gor(T ) is reducible. We also show that the Hilbert function of a codimension four Gorenstein Artin algebra can have an arbitrarily long constant part with...