In this article we give a uniform proof why the shift map on Floer homology trajectory spaces is scale smooth. This works for various homologies, periodic, Lagrangian, Hyperk\"ahler, elliptic or parabolic, and uses Hilbert space valued Sobolev theory.

Abstract In this article, we consider an analogue of Arakelov theory arithmetic surfaces over a trivially valued field. particular, establish Hilbert–Samuel theorem and study the effectivity up to $\mathbb R$-linear equivalence pseudoeffective metrised R$-divisors.

An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discret...

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operatorvalued kernels. We propose a general principle for Operator-valued Random Four...

In this paper, a new soft computing group decision method based on the concept of compromise ratio is introduced for determining decision makers (DMs)' weights through the group decision process under uncertainty. In this method, preferences and judgments of the DMs or experts are expressed by linguistic terms for rating the industrial alternatives among selected criteria as well as the relativ...

This paper extends the theory of Zen spaces (weighted Hardy/Bergman on right-hand half-plane) to Hilbert-space valued case, and describes multipliers them; it is shown that methods H∞ control can therefore be extended certain weighted L2 input output spaces. Next, case retarded delay systems with operator-valued transfer functions analysed, dependence structure determined by developing an exten...

We show several examples of n.a. valued fields with involution. Then, by means of a field of this kind, we introduce “n.a. Hilbert spaces” in which the norm comes from a certain hermitian sesquilinear form. We study these spaces and the algebra of bounded operators which are defined on them and have an adjoint. Essential differences with respect to the usual case are observed.