Abstract Let $$\mathbb {D}$$ D denote the unit disk of complex plane and let $$\mathcal {A}^2(\mathbb {D})$$ A 2 ( ) be Bergman space that consists those analytic functions on are integrable squar...

Let $\mathcal{X}$ be a separable Hilbert space with norm $\|\cdot\|$ and let $T>0$. $Q$ linear, self-adjoint, positive, trace class operator on $\mathcal{X}$, $F:\mathcal{X}\rightarrow \mathcal{X}$ (smooth enough) function $W(t)$ $\mathcal{X}$-valued cylindrical Wiener process. For $\alpha\in [0,1/2]$ we consider the $A:=-(1/2)Q^{2\alpha-1}:Q^{1-2\alpha}(\mathcal{X})\subseteq \mathcal{X}\righta...

This work concerns surjective maps $\varphi\colon R\to S$ of commutative noetherian local rings with kernel generated by a regular sequence that is part minimal generating set for the maximal ideal $R$. The main result provides criteria detecting such exceptional complete intersection in terms lattices thick subcategories derived category complexes finite length homology. A key input characteri...

Abstract The fast growing solutions of the following linear differential equation $$(*)$$ ( ∗ ) is investigated by using a more general scale $${[p,q]_{,\varphi }}$$ [ p , <mml:m...

In this work we set up the generating function of ultimate time survival probability $\varphi(u+1)$, where $$\varphi(u)=\mathbb{P}\left(\sup_{n\geqslant 1}\sum_{i=1}^{n}\left(X_i-\kappa\right)<u\right)$$ and $u\in\mathbb{N}_0,\,\kappa\in\mathbb{N}$, random walk $\left\{\sum_{i=1}^{n}X_i,\,n\in\mathbb{N}\right\}$ consists independent identically distributed variables $X_i$, which are non-negativ...