相关论文: A simple construction of potential operators for c…

Let G be a compact connected semisimple Lie group and let H\subset G be a closed connected subgroup such that rank(G)=rank(H) and G/H is a symmetric space. Given an irreducible representation of H, we define a Dirac operator D and determine…

We study norm attainment for multilinear operators and homogeneous polynomials between Banach spaces, as well as for positive multilinear operators between Banach lattices. We establish multilinear and polynomial versions of [23, Theorem B]…

We study the inverse spectral problem for periodic Schr\"odinger opera\-tors of kind $- \frac{1}{2} \hbar^2 \Delta_x + V(x)$ on the flat torus $\Bbb T^n := (\Bbb R / 2 \pi \Bbb Z)^n$ with potentials $V \in C^{\infty} (\Bbb T^n)$. We show…

In this paper we provide a positive answer to a conjecture due to A. J. Di Scala, A. Loi, H. Hishi (see [3, Conjecture 1]) claiming that a simply-connected homogeneous K\"ahler manifold M endowed with an integral K\"ahler form $\mu\omega$,…

We establish a compensated compactness theorem in the microlocal and geometric analytic framework. For a weakly $L^2_{\rm loc}$-convergent sequence of sections of a vector bundle over a semi-Riemannian manifold whose image under a…

Let $E$ be a sublattice of a vector lattice $F$. A continuous operator $T$ from the vector lattice $E$ into a normed vector space $X$ is said to be $\tilde{o}$rder-norm continuous whenever $x_\alpha\xrightarrow{Fo}0$ implies…

We prove that a nonzero idempotent is zero-diagonal if and only if it is not a Hilbert-Schmidt perturbation of a projection, along with other useful equivalences. Zero-diagonal operators are those whose diagonal entries are identically zero…

To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…

In this note we prove that a homomorphism from a compact connected simple Lie group with the norm topology to any separable SIN group is automatically continuous. This generalizes a result by Dowerk and Thom. Further, we prove some…

We study a specific family of symmetric norms on the algebra $\mathcal B(\mathcal H)$ of operators on a separable infinite-dimensional Hilbert space. With respect to each symmetric norm in this family the identity operator fails to attain…

The separate tasks of denoising, least squares expectation, and manifold learning can often be posed in a common setting of finding the conditional expectations arising from a product of two random variables. This paper focuses on this more…

In this paper, we prove that, if a full irreducible infinite dimensional anti-Kaehler isoparametric submanifold of codimension greater than one has $J$-diagonalizable shape operators, then it is homogeneous.

We prove that, for a suitable choice of real numbers $a, b$, every operator from $\ell_2$ to $X_{a,b}$ and from $X_{a,b}$ to $\ell_2$ must be compact, where $X_{a,b}$ is the Bourgain- Delbaen's space.

The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators…

In this paper we consider a large class of fully nonlinear integro-differential equations. The class of our nonlocal operators we consider is not spatial homogeneous and we put mild assumptions on its kernel near zero. We prove the H\"older…

We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of $\mathcal{L}_1$ and…

We prove sufficient conditions in order to obtain a sharp G\aa rding inequality for pseudo-differential operators acting on vector-valued functions on compact Lie groups. As a consequence, we obtain a sharp G\aa rding inequality for compact…

In this short report we estimate and calculate the exact value of norms of multilinear integral operators having homogeneous kernel, acting between two Grand Lebesgue Spaces.

We develop the compactness theory of multilinear singular integrals on product spaces using a modern point of view. The first main result is a compact $T1$ theorem for multilinear Calder\'{o}n--Zygmund operators on product spaces. More…

Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded domains, focusing on those with integrable kernels having…