Sentence examples for by a linear operator from inspiring English sources

The relation between and can be described by a linear operator transforming into such that: (40).

The LTV system is described by a linear operator that maps an input signal into an output signal r(t), related by the following noise-free relationship, (1).

Let X be a Banach space and (e^{At}) the (C_{0} -semigroup generated by a linear operator A. In this section, we recall some related results about semigroups and compact sets from [9, 10} -semigrouphich will be used in this paper.

We assume that the true image f is defined on an index set Ω and its observed version g on an index set Λ. We also assume that g is blurred from f by a linear operator ({mathcal T}colon ell ^{2}(Omega) to ell ^{2}(Lambda)) and further corrupted by pixel-wisely independent Poisson noise: g_{i_{1},i_{2}} sim text{Poisson}left(({mathcal T}mathbf{f})_{i_{1},i_{2}}right), quad (i_{1},in{2}) in Lambda.

In the present paper, we obtain some mapping and inclusion properties for subclasses of analytic functions by using a linear operator defined by the Gaussian hypergeometric function.

By defining a linear operator acting on the coefficient matrix of the filter, the optimality condition of the design problem is expressed as a linear operator equation.

Denote by (L_{k}) a linear operator from (mathbb{R}^{m_{k}}) to (mathbb{R}^{m_{k}}) such that the rank of (L_{k}) is at most (n_{k}) and gamma_{m_{k}}bigl(bigl{ yin mathbb{R}^{m_{k}} vert Vert V_{k} y-L_{k}yVert >2 lambda_{n_{k},sigma_{k}} bigr} bigr) leq sigma_{k}.

By elementary functional analysis, a linear operator between normed spaces is bounded if and only if it is continuous, and the boundedness is trivially also equivalent to the Lipschitz-continuity.

By elementary functional analysis, a linear operator between normed spaces is bounded if and only if it is continuous, and the boundedness is trivially also equivalent to the Lipschitz-continuity. So, our result for composition operators in hyperbolic spaces is the correct and natural generalization of the linear operator theory.

Let L X, Y) be the set of all linear continuous operators from X into Y, denoted 〈t, x〉 by the value of a linear operator t ∈ L X, Y) at x ∈ X, and C X X → 2 Y be a set-valued mapping such that C x) is a proper closed convex cone for all x ∈ X with int C ( x ) ≠ ∅.

The approximation of a linear operator by, that is, a concatenation of an analysis operation, an element-wise multiplication, and a synthesis operation, appears in the literature under the name Gabor multiplier [27].