Sentence examples for functions of the operator from inspiring English sources

They established that, if q ∈ C 4 [ 0, 1 ], q ( 1 ) ≠ q ( 0 ), then the root functions of the operator L ( q ) form a Riesz basis in L 2 [ 0, 1 ], where L ( q ) denotes the operator generated by (1) and the periodic boundary conditions.

(2.14) which are the characteristic functions of the operators (L q_{j},h_{0},h_{j})=:L_{j}).

We note that in [6, 10, 11], using the obtained asymptotic formulas for eigenvalues and eigenfunctions, the basis properties of the root functions of the operators were investigated.

There are many examples of activation functions which are used in practice, notably the periodization of the Wendland functions, or Green's functions of the operators ({ -Delta )^{ -Delta for which this condition is not satisfied.

An operator that has this characteristic is known as a truth-functional operator, and a proposition formed by such an operator is called a truth function of the operator's argument(s).

In the next section, the Green's function of the operator (A=A^{x}) defined by formula (4) is studied.

The second approach is based on a splitting of the operators, and the time integration method is function of the operator considered (fractional step schemes).

Let G x, y), x, y ∈, Rd denote the Green's function of the operator −12Δ + V, where V is a continuous, periodic function.

For (gammain(1,2]), (G_{gamma} x,s)) is the Green function of the operator (urightarrow-D^{gamma}u), with boundary data (lim_{xrightarrow0^D^{gamma -1}u(x)=u(1)=0).

In this section, we briefly recall some basic results for the Green function of the operator (Delta_{alpha}=- -Delta)^{alpha/2}) anDelta_{alpha}=- -Deltasheet.

The analytic index of a generalized Toeplitz operator defined in terms of a trace is shown to be equal to minus the topological index of the symbol function of the operator, a result that extends some well-known index theorems.