相关论文: Hyper innerproduct spaces II

In this note we observe that the notion of an induced representation has an analog for quasi-actions. We then use induced quasi-actions to refine some earlier rigidity results for product spaces.

The paper deals with extension of bounded bilinear maps$.$ It gives a necessary and sufficient condition for extending a bounded bilinear map on the Cartesian product of subspaces of Banach spaces$.$ This leads to a full characterization…

We define the secondary Hochschild complex for an entwining structure over a commutative $k$-algebra $B$. We show that this complex carries the structure of a weak comp algebra. We obtain two distinct cup product structures for the…

We introduce a n-term quadrature to integrate inner products of n functions, as opposed to a Gaussian quadrature to integrate 2n functions. We will characterize and provide computational tools to construct the inner product quadrature, and…

This work presents a rigorous characterization of inner products on the Hilbert space $S_2$ of Hilbert--Schmidt operators. We first deal with a general setting of continuous sesquilinear forms on a Hilbert space $\mathcal H$, and provide a…

We show that the image of repeated differentiation on weak cusp forms is precisely the subspace which is orthogonal to the space of weakly holomorphic modular forms. This gives a new interpretation of the weakly holomorphic Hecke…

In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.

This habilitation thesis centres on linearisation of vector-valued functions which means that vector-valued functions are represented by continuous linear operators. The first question we face is which vector-valued functions may be…

We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…

We study the sum-product problem for the planar hypercomplex numbers: the dual numbers and double numbers. These number systems are similar to the complex numbers, but it turns out that they have a very different combinatorial behavior. We…

We usually define an algebraic structure by a set, some operations defined on this set and some propositions that the algebraic structure must validate. In some cases, we can replace these propositions by an algorithm on terms constructed…

We discuss the notion of an inner function for spaces of analytic functions in multiply connected domains in $\mathbb{C}$, giving a historical overview and comparing several possible definitions. We explore connections between inner…

Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…

In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

In this paper we introduce a generalization of Hilbert C-modules which are pre- Finsler module namely C-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will…

This paper provides conditions (i) to distinguish weak supercyclicity form supercyclicity for operators acting on normed and Banach spaces, and also (ii) to ensure when weak supercyclicity implies weak stability.

We start by showing how to approximate unitary and bounded self-adjoint operators by operators in finite dimensional spaces. Using ultraproducts we give a precise meaning for the approximation. In this process we see how the spectral…

If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.

We introduce a wide category of superspaces, called locally finitely generated, which properly includes supermanifolds but enjoys much stronger permanence properties, as are prompted by applications. Namely, it is closed under taking finite…