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Starting with an additive process $(Y_t)_{tgeq0}$, it is in certain cases possible to construct an adjoint process $(X_t)_{tgeq0}$ which is itself additive. Moreover, assuming that the transition densities of $(Y_t)_{tgeq0}$ are controlled by a natural pair of metrics $mathrm{d}_{psi,t}$ and $delta_{psi,t}$, we can prove that the transition densities of $(X_t)_{tgeq0}$ are controlled by the metrics $delta_{psi,1/t}$ replacing $mathrm{d}_{psi,t}$ and $mathrm{d}_{psi,1/t}$ replacing $delta_{psi,t}$.
The paper is devoted to a development of the theory of self-adjoint operators in Krein spaces (J-self-adjoint operators) involving some additional properties arising from the existence of C-symmetries. The main attention is paid to the recent notion
Let $X$ and $Y$ be Banach spaces, let $mathcal{A}(X)$ stands for the algebra of approximable operators on $X$, and let $Pcolonmathcal{A}(X)to Y$ be an orthogonally additive, continuous $n$-homogeneous polynomial. If $X^*$ has the bounded approximatio
Let $J$ and $R$ be anti-commuting fundamental symmetries in a Hilbert space $mathfrak{H}$. The operators $J$ and $R$ can be interpreted as basis (generating) elements of the complex Clifford algebra ${mathcal C}l_2(J,R):={span}{I, J, R, iJR}$. An arb
We compute the deficiency spaces of operators of the form $H_A{hat{otimes}} I + I{hat{otimes}} H_B$, for symmetric $H_A$ and self-adjoint $H_B$. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumanns theory. The
Let $G$ be a compact group, let $X$ be a Banach space, and let $Pcolon L^1(G)to X$ be an orthogonally additive, continuous $n$-homogeneous polynomial. Then we show that there exists a unique continuous linear map $Phicolon L^1(G)to X$ such that $P(f)