相关论文: Integral estimates for the trace of symmetric oper…

This thesis is devoted to asymptotic norm estimates for oscillatory integral operators acting on the L^2 space of functions of one real variable. The operators in question have compact support and an oscillatory kernel of the form exp(i…

Let $\mathscr{X}$ be a complex Banach space and $\mathcal{L}(\mathscr{X})$ be the algebra of all bounded linear operators on $\mathscr{X}$. For a given elementary operator $\Phi$ of length $2$ on $\mathcal{L}(\mathscr{X})$, we determine…

In the context of continuous zooming systems $f:M \to M$ on a compact metric space $M$, which include the non-uniformly expanding ones, possibly with the presence of a critical set, with the zooming set dense in $M$, we prove that any…

In this paper we obtain a splitting theorem for the symmetric diffusion operator $\Delta_\phi=\Delta-\left<\nabla\phi,\nabla \right>$ and a non-constant $C^3$ function $f$ in a complete Riemannian manifold $M$, under the assumptions that…

Let $x:M^m\to \bar M$, with $m\geq 3$, be an isometric immersion of a complete noncompact manifold $M$ in a complete simply-connected manifold $\bar M$ with sectional curvature satisfying $-c^2\leq K_{\bar M}\leq 0$, for some constant $c$.…

We give sufficient and necessary geometric conditions, guaranteeing that an immersed compact closed manifold $\Sigma^m\subset \R^n$ of class $C^1$ and of arbitrary dimension and codimension (or, more generally, an Ahlfors-regular compact…

Let $\mathfrak{M}$ be a semifinite von Neumann algebra on a Hilbert space equipped with a faithful normal semifinite trace $\tau$. A closed densely defined operator $x$ affiliated with $\mathfrak{M}$ is called $\tau$-measurable if there…

Let $M$ be a closed (compact with no boundary) spherical $CR$ manifold of dimension $2n+1$. Let $\widetilde{M}$ be the universal covering of $M.$ Let $% \Phi $ denote a $CR$ developing map {equation*} \Phi :\widetilde{M}\rightarrow S^{2n+1}…

We investigate the traceability of positive integral operators on $L^2(X,\mu)$ when $X$ is a Hausdorff locally compact second countable space and $\mu$ is a non-degenerate, $\sigma$-finite and locally finite Borel measure. This setting…

We establish two global subellipticity properties of positive symmetric second-order partial differential operators on $L_2(\Ri^d)$. First, if $m \in \Ni$ then we consider operators $H_0$ with coefficients in $W^{m+1,\infty}(\Ri^d)$ and…

For a given $\delta$, $0<\delta<1$, a Blaschke sequence $\sigma=\{\lambda_j\}$ is constructed such that every function $f$, $f\in H^\infty$, having $\delta<\delta_f=\inf_{\lambda\in\sigma}|f(\lambda)|\le\|f\|_\infty\le1$ is invertible in…

We show that a complete $m$-dimensional immersed submanifold $M$ of $\mathbb{R}^{n}$ with $a(M)<1$ is properly immersed and have finite topology, where $a(M)\in [0,\infty]$ is an scaling invariant number that gives the rate that the norm of…

Let M be a closed spin manifold of dimension congruent to 3 modulo 4. We give a simple proof of the fact that the space of metrics on M with invertible Dirac operator is either empty or it has infinitely many path components.

Given $r_0>0$, $I\in \mathbb{N}\cup \{0\}$ and $K_0,H_0\geq 0$, let $X$ be a complete Riemannian $3$-manifold with injectivity radius $\mbox{Inj}(X)\geq r_0$ and with the supremum of absolute sectional curvature at most $K_0$, and let…

Let $\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be a quaternionic normal operator with the domain $\mathcal{D}(T) \subset \mathcal{H}$. Then for a fixed unit imaginary quaternion $m$, there exists a Hilbert basis…

An $f$-structure on a manifold $M$ is an endomorphism field $\phi\in\Gamma(M,\End(TM))$ such that $\phi^3+\phi=0$. Any $f$-structure $\phi$ determines an almost CR structure $E_{1,0}\subset T_\C M$ given by the $+i$-eigenbundle of $\phi$.…

We consider a class of non-doubling manifolds $\mathcal{M}$ that are the connected sum of a finite number of $N$-dimensional manifolds of the form $\mathbb{R}^{n_{i}} \times \mathcal{M}_{i}$. Following on from the work of Hassell and the…

Let $(G,+)$ be a topological abelian group with a neutral element $e$ and let $\mu : G\longrightarrow\mathbb{C}$ be a continuous character of $G$. Let $(\mathcal{H}, \langle \cdot,\cdot \rangle)$ be a complex Hilbert space and let…

We use induction and interpolation techniques to prove that a composition operator induced by a map $\phi$ is bounded on the weighted Bergman space $\A^2_\alpha(\mathbb{H})$ of the right half-plane if and only if $\phi$ fixes $\infty$…

Let $M$ be Hadamard manifold with sectional curvature $K_{M}\leq-k^{2}$, $k>0$. Denote by $\partial_{\infty}M$ the asymptotic boundary of $M$. We say that $M$ satisfies the strict convexity condition (SC condition) if, given…