In this paper, we first derive some results by using the Gelfand spectrum and spectrum in FLM algebras. Then, the characterizations of multiplicative linear mappings are also discussed in these algebras.

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

In this paper, we characterize completely the global hypoellipticity and solvability in sense of Komatsu (of Roumieu Beurling types) constant-coefficient vector fields on compact Lie groups. We also analyze influence perturbations by lower-order terms preservation these properties.

The notion of $f$-derivations of UP-algebras is introduced, some useful examples are discussed, and related properties are investigated. Moreover, we show that the fixed set and the kernel of $f$-derivations are UP-subalgebras of UP-algebras,and also give examples to show that the two sets are not UP-ideals of UP-algebras in general.

 We study the notion of bounded approximate Connes-amenability for‎ ‎dual Banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎We show that bounded approximate‎ ‎Connes-amenability of dual Banach algebras forces them to be unital‎. ‎For a separable dual Banach algebra‎, ‎we prove that bounded‎ ‎approximate Connes-amenability implies sequential approximat...

Abstract. There has been a surge of interest of late in an old result of Nyman and Beurling giving a Hilbert space formulation of the Riemann hypothesis. Many authors have contributed to this circle of ideas, culminating in a beautiful refinement due to Baez-Duarte. The purpose of this little survey is to dis-entangle the resulting web of complications, and reveal the essential simplicity of th...

This paper presents new results for the modulus of families of walks on a graph—a discrete analog of the modulus of curve families due to Beurling and Ahlfors. Particular attention is paid to the dependence of the modulus on its parameters. Modulus is shown to generalize (and interpolate among) three important quantities in graph theory: shortest path, effective resistance, and max-flow or min-...

An inner-outer factorization theorem for linear time-varying systems is obtained via an extension of the classical Beurling-Lax theorem to the time-varying context. This provides characteristic features of the inner factor, which can be used to compute realizations of the inner and outer factors from a realization of the given transfer operator. The resulting algorithm is unidirectional in time...

Let ρ(x) = x − [x], χ = χ (0,1). In L2(0, ∞) consider the subspace B generated by {ρa|a ≥ 1} where ρa(x) := ρ 1 ax. By the Nyman-Beurling criterion the Riemann hypothesis is equivalent to the statement χ ∈ B. For some time it has been conjectured, and proved in this paper, that the Riemann hypothesis is equivalent to the stronger statement that χ ∈ B nat where B nat is the much smaller subspace...