This article is one of squeal papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in E n to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a conformal surface case and completely ...

This paper concerns the smoothness of Tauberian constants of maximal operators in the discrete and ergodic settings. In particular, we define the discrete strong maximal operator M̃S on Z by M̃Sf(m) := sup 0∈R⊂Rn 1 #(R ∩ Zn) ∑ j∈R∩Zn |f(m+ j)|, m ∈ Z, where the supremum is taken over all open rectangles in R containing the origin whose sides are parallel to the coordinate axes. We show that the a...

The convolution in R with |x|−n is a very singular operator. Endowed with a proper normalization, and regarded as a limit of Riesz potentials, it is equal to Dirac’s distribution δ. However, a different normalization turns the non-linear operator: Ef = exp( −2 |Sn−1| |x|−n ∗ f), into a remarkable transformation. Its long history (in one dimension) and some of its recent applications in higher d...

On a given complex manifold X, there are two natural cohomologies to consider. One is the de Rham Cohomology which can be defined on a general, possibly non complex, manifold. The second one is the Dolbeault cohomology which uses the complex structure. We’ll quickly go over the definitions of these cohomologies in order to set notation but for a precise discussion I recommend Huybrechts or Well...

Let H denote a separable, infinite-dimensional complex Hilbert space. A two-sided ideal / of operators on H possesses the generalized Fuglede property (GFP) if, for every normal operator N and every X e L(H), NX XN e I implies N*X XN* e /. Fuglede's Theorem says that / = {0} has the GFP. It is known that the class of compact operators and the class of Hilbert-Schmidt operators have the GFP. We ...

‎in this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎to this end‎, ‎we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎first‎, ‎we put forward the concept of operator-valued tensors and extend semi-riemannian...

‖u− Ihu‖L2(T ) ≤cThT ‖∇ku‖L2(ω̃T ), ‖u− Ihu‖L2(E) ≤cEh E ‖∇ku‖L2(ω̃E). Here, k ∈ {1, 2}, Ih is some quasi-interpolation operator, T and E are a simplex and a face thereof, hT and hE measure the size of T and E, and ω̃T and ω̃E are neighbourhoods of T and E which should be as small as possible. Note that the interpolate Ihu never needs to be computed explicitely. Moreover, for problems in two and th...

It was observed in [Su5] that the spectrum of a periodic Schrodinger operator on a Riemannian manifold has band structure if the transformation group acting on the manifold satisfies the Kadison property (see below for the definition). Here band structure means that the spectrum is a union of mutually disjoint, possibly degenerate closed intervals, such that any compact subset of R meets only f...

The intertwining operator, κ, in the isospectrality proof of [Sz1, Sz2] 1 2 3 does not appear in the right form. The correct operator associates rather the Z-Fourier transforms of the functions corresponded to each other by this κ. In this note the isospectralities are established by means of this redefined operator. New isospectrality examples are also constructed. They live on sphere×balland ...

For an operator T acting from an infinite-dimensional Hilbert space H to a normed space Y we define the upper AMD-number δ(T ) and the lower AMD-number δ(T ) as the upper and the lower limit of the net (δ(T |E))E∈FD(H) , with respect to the family FD(H) of all finite-dimensional subspaces of H. When these numbers are equal, the operator is called AMDregular. It is shown that if an operator T is...