Linear correlations of multiplicative functions
نویسندگان
چکیده
منابع مشابه
Learning Linear Functions with Quadratic and Linear Multiplicative Updates
We analyze variations of multiplicative updates for learning linear functions online. These can be described as substituting exponentiation in the Exponentiated Gradient (EG) algorithm with quadratic and linear functions. Both kinds of updates substitute exponentiation with simpler operations and reduce dependence on the parameter that specifies the sum of the weights during learning. In partic...
متن کاملOn multiplicative (strong) linear preservers of majorizations
In this paper, we study some kinds of majorizations on $textbf{M}_{n}$ and their linear or strong linear preservers. Also, we find the structure of linear or strong linear preservers which are multiplicative, i.e. linear or strong linear preservers like $Phi $ with the property $Phi (AB)=Phi (A)Phi (B)$ for every $A,Bin textbf{M}_{n}$.
متن کاملAlmost multiplicative linear functionals and approximate spectrum
We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...
متن کاملArithmetical Functions I: Multiplicative Functions
Truth be told, this definition is a bit embarrassing. It would mean that taking any function from calculus whose domain contains [1,+∞) and restricting it to positive integer values, we get an arithmetical function. For instance, e −3x cos2 x+(17 log(x+1)) is an arithmetical function according to this definition, although it is, at best, dubious whether this function holds any significance in n...
متن کاملMultiplicative Distance Functions
We call φ the root function of Φ. The continuity of Φ implies that (1.2) φ(γ) → |γ| as |γ| → ∞. Moreover the converse is true, if φ is continuous and satisfies this asymptotic formula, then the function Φ formed as in (1.1) is a multiplicative distance function. Theorem 1.1. A continuous function φ : C → [0,∞) is the root function of a multiplicative distance function iff it satisfies (1.2). Ar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2020
ISSN: 0024-6115,1460-244X
DOI: 10.1112/plms.12309