The problem of recovering a first-order scalar differential operator acting on vector-valued functions from its kernel

1994 ◽  
Vol 72 (6) ◽  
pp. 3425-3427
Author(s):  
V. G. Osmolovskii
Keyword(s):  
Differential Operator ◽  
First Order ◽  
Vector Valued Functions ◽  
Vector Valued

Random Response Analysis of Vibration Transfer Path Systems with Translational and Rotational Motions

2013 ◽  
Vol 423-426 ◽  
pp. 1543-1547
Author(s):  
Wei Zhao ◽  
Na Zhou ◽  
Yi Min Zhang
Keyword(s):  
Random Vibration ◽  
Response Analysis ◽  
Random Response ◽  
First Order ◽  
Transfer Path ◽  
Mathematical Expressions ◽  
Path System ◽  
Rotational Motions ◽  
Vector Valued Functions ◽  
Vector Valued

This paper based on the generalized probabilistic perturbation finite element method solves the random response analysis problem of vibration transfer path systems with translational and rotational motions. The effective random response analysis approaches are achieved using Kronecker algebra, matrix calculus, generalized second moment technique of vector-valued functions and matrix-valued functions. For the vibration transfer path system with multi-dimensional paths, the random response is described correctly and expressly in time domain as uncertain factors, which include mass, damping, stiffness and position, are considered. The mathematical expressions of the first order and second order moments for the random vibration response of vibration transfer path are obtained. According to the corresponding numerical example, the results of calculation are consistent with the results of Monte-Carlo simulation, which shows the method is feasible theoretically.

scholarly journals On the boundedness of square function generated by the Bessel differential operator in weighted Lebesque Lp,α spaces

2018 ◽  
Vol 16 (1) ◽  
pp. 730-739
Author(s):  
Simten Bayrakci
Keyword(s):  
Differential Operator ◽  
Weak Type ◽  
Half Line ◽  
Square Function ◽  
Plancherel Theorem ◽  
Bessel Differential Operator ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractIn this paper, we consider the square function$$\begin{array}{} \displaystyle (\mathcal{S}f)(x)=\left( \int\limits_{0}^{\infty }|(f\otimes {\it\Phi}_{t})\left( x\right) |^{2}\frac{dt}{t}\right) ^{1/2} \end{array} $$associated with the Bessel differential operator $\begin{array}{} B_{t}=\frac{d^{2}}{dt^{2}}+\frac{(2\alpha+1)}{t}\frac{d}{dt}, \end{array} $α > −1/2, t > 0 on the half-line ℝ+ = [0, ∞). The aim of this paper is to obtain the boundedness of this function in Lp,α, p > 1. Firstly, we proved L2,α-boundedness by means of the Bessel-Plancherel theorem. Then, its weak-type (1, 1) and Lp,α, p > 1 boundedness are proved by taking into account vector-valued functions.

Nonselfadjoint Schrödinger operators with singular first-order coefficients

1984 ◽  
Vol 96 (3-4) ◽  
pp. 323-329 ◽  
Author(s):  
Tosio Kato
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Real Vector ◽  
First Order ◽  
Vector Valued Functions ◽  
Complex Valued ◽  
Vector Valued

SynopsisSchrödinger operators of the form T = (i grad + b(x))2 + a(x) · grad + q(x) in Rm are considered, where a, b ate real vector-valued functions and q is a scalar complex-valued function. It is shown that T is essentially quasi-m-accretive in L2(Rm) if (1 + #x2223;∣)−1a ∈ L4 + L∞, div a ∈ L∞, , and Re q ≧ 0. The proof is elementary.

scholarly journals Farkas-Type Results for Vector-Valued Functions with Applications

2017 ◽  
Vol 173 (2) ◽  
pp. 357-390 ◽  
Author(s):  
N. Dinh ◽  
M. A. Goberna ◽  
M. A. López ◽  
T. H. Mo
Keyword(s):  
Vector Valued Functions ◽  
Vector Valued

scholarly journals Diameter-preserving linear bijections of function spaces

2001 ◽  
Vol 70 (3) ◽  
pp. 323-336 ◽  
Author(s):  
T. S. S. R. K. Rao ◽  
A. K. Roy
Keyword(s):  
Maximal Ideal ◽  
Convex Set ◽  
Compact Convex ◽  
Extreme Points ◽  
Continuous Functions ◽  
Ideal Space ◽  
Function Algebras ◽  
Compact Convex Set ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractIn this paper we give a complete description of diameter-preserving linear bijections on the space of affine continuous functions on a compact convex set whose extreme points are split faces. We also give a description of such maps on function algebras considered on their maximal ideal space. We formulate and prove similar results for spaces of vector-valued functions.

Laplace transforms of polynomially bounded vector-valued functions and semigroups of operators

1997 ◽  
Vol 98 (1) ◽  
pp. 189-207 ◽  
Author(s):  
R. DeLaubenfels ◽  
Z. Huang ◽  
S. Wang ◽  
Y. Wang
Keyword(s):  
Laplace Transforms ◽  
Semigroups Of Operators ◽  
Vector Valued Functions ◽  
Vector Valued

scholarly journals THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS

2014 ◽  
Vol 57 (1) ◽  
pp. 17-82 ◽  
Author(s):  
TUOMAS P. HYTÖNEN ◽  
ANTTI V. VÄHÄKANGAS
Keyword(s):  
Singular Integrals ◽  
Local Version ◽  
Square Functions ◽  
Property A ◽  
Martingale Differences ◽  
Umd Spaces ◽  
Function Lattice ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Similar Extension

AbstractWe extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, ‘vector-valued’ means ‘taking values in a function lattice with the UMD (unconditional martingale differences) property’. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local version requires several elaborations of the previous techniques, and raises new questions about the limits of the vector-valued theory.

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