Abstract The Jánossy density for a determinantal point process is the probability that an interval $I$ contains exactly $p$ points except those at $k$ designated loci. associated with integrable kernel $\mathbf{K}\doteq (\varphi(x)\psi(y)-\psi(x)\varphi(y))/(x-y)$ shown to be expressed as Fredholm determinant $\mathrm{Det}(\mathbb{I}-\tilde{\mathbf{K}}|_I)$ of transformed $\tilde{\mathbf{K}}\do...

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see cite{Sc, S}), and studdied for example in cite{M} and cite{I}. In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this concept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and...

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

let $mathcal{a}$ be a banach algebra and $mathcal{m}$ be a banach $mathcal{a}$-bimodule. we say that a linear mapping $delta:mathcal{a} rightarrow mathcal{m}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{a} rightarrow mathcal{m}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{a}$. giving some facts concerning general...

Let $$\Omega \subset {\mathbb {C}}^n$$ be a smooth bounded pseudoconvex domain and $$A^2 (\Omega )$$ denote its Bergman space. $$P:L^2(\Omega )\longrightarrow A^2(\Omega the projection. For measurable $$\varphi :\Omega \longrightarrow \Omega $$ , projected composition operator is defined by $$(K_\varphi f)(z) = P(f \circ \varphi )(z), z \in f\in A^2 ).$$ In 1994, Rochberg studied boundedness of...

We provide a boundedness criterion for the integral operator $$S_{\varphi }$$ on fractional Fock–Sobolev space $$F^{s,2}({{\mathbb {C}}}^n)$$ , $$s\ge 0$$ where (introduced by Zhu [18]) is given $$\begin{aligned} S_{\varphi }F(z):= \int _{{\mathbb {C}}^n} F(w) e^{z \cdot \bar{w}} \varphi (z- \bar{w}) d\lambda (w) \end{aligned}$$ with $$\varphi $$ in Fock $$F^2({{\mathbb {C}}^n})$$ and $$d\lambd...