Theorem 1. Let M be a compact manifold, E and F be two (smooth) vector bundles over M , and P : C∞(M ;E) → C∞(M ;F ) be a differential operator (with smooth coefficients) of order n. Assume that P is elliptic, in the sense defined in the next section. Then: 1. The operator P (or rather its relevant extension) is Fredholm W n 2 (M ;E)→ L(M ;F ). Here W n 2 is a Sobolev space (introduced below). ...

This paper studies the absolute stability of a sampled-data, m-user haptic virtual environment (HVE) system based on the discrete-time circle criterion. Depending on the task being performed by an operator, the passivity of the operator is influenced. We provide a framework for the system stability analysis in which the operator is allowed to exhibit passive or active behavior. In this paper, t...

Uni6n M a t d t i c a Argentina Vol. 35 1990. Introduction The main purpose of this paper is to give a comprehensive motivation, with most of the key ideas used in the recent work by Garroni and Menaldi [lo], on the construction of the Green function G(z, t, (, r) for an integro-differential initial boundary value problem, when the differential operator is a second-order parabolic operator not ...

We outline a method for controlling a model for the return times operator. For more information about how this model operator relates to the return times theorem, see the summary by Patrick LaVictoire in these conference proceedings. 1.1 Notation and prior results For a sequence (xj)j ⊆ C, define ||xj ||Ṽ r k = sup M,k0,...,kM ( M ∑ m=1 |xkm − xkm−1 | ) 1 r

The following limit result holds for the weak–type (1,1) constant of dilation-commuting singular integral operator T in Rn: for f ∈ L1(Rn), f ≥ 0, lim λ→0 λ m{x ∈ R : |Tf(x)| > λ} = 1 n ∫ Sn−1 |Ω(x)|dσ(x)‖f‖1. For the maximal operator M , the corresponding result is lim λ→0 λ m{x ∈ R : |Mf(x)| > λ} = ‖f‖1.

ALINA ALB LUPAS¸Abstract. In the present paper we establish several differential superordinations regarding the new operator RD m λ,α defined by using the generalized S˘ al˘ agean operator D m λ f (z) and Ruscheweyh derivative R m f ∞ j=n+1 a j z j , z ∈ U }. A number of interesting consequences of some of these superordination results are discussed. Relevant connections of some of the new resu...

An entangled ergodic theorem was introduced in [1] in connection with the quantum central limit theorem, and clearly formulated in [6]. Namely, let U be a unitary operator on the Hilbert space H, and for m ≥ k, α : {1, . . . , m} 7→ {1, . . . , k} a partition of the set {1, . . . , m} in k parts. The entangled ergodic theorem concerns the convergence in the strong, or merely weak (s–limit, or w...

We compute the spectra of Laplace-Beltrami operator, connection Laplacian on 1-forms and Einstein operator symmetric 2-tensors sine-cone over a positive manifold $(M, g)$. conclude under which conditions $(M,g)$, is dynamically stable singular Ricci-de Turck flow rigid as

We consider the Schr\"odinger operator on halfline with potential $(m^2-\frac14)\frac1{x^2}$, often called Bessel operator. assume that $m$ is complex. study domains of various closed homogeneous realizations In particular, we prove domain its minimal realization for $|\Re(m)|<1$ and unique $\Re(m)>1$ coincide second order Sobolev space. On other hand, if $\Re(m)=1$ space a subspace infinite co...

Making use of a differential operator the author investigate the various impartant properties and characteristics of the subclass Tj(n,m, p, q, α) (p, j,m ∈ N = {1, 2, . . .}, q, n ∈ N0 = N ∪ {0}, 0 ≤ α < p − q) of p-valently analytic functions with negative coefficients. Finally, several applications involving an integral operator and certain fractional calculus operators are also considered.