Sentence examples for integral kernel from inspiring English sources

Now let us consider the strong integral kernel case.

Firstly, let us consider the weakly integral kernel case.

A basic role is played by an integral kernel operator which is a superposition of creation and annihilation operators with operator-valued distributions as integral kernel.

The following corollary of Theorem 7 is concerned with the Riemann-Liouville fractional integral kernel.

Let (D_{t}^{k} z)) be the integral kernel of the operator (D_{t}^{k}).

The operators can either be Radon transforms or averaging operators with multiparameter fractional integral kernel.

Since the integral kernel has this kind of singularity, equation (11) is said to have a weakly singular kernel.

Since the integral kernel of (mathcal {K}) is positive, the following statement, sometimes called Jentsch's theorem, applies.

A Green's function is an integral kernel that can be used to solve inhomogeneous differential equations with boundary conditions.

Applications to Schrödinger operators with rather general random scalar potentials include a rigorous justification of an integral-kernel representation of their integrated density of states a relation frequently used in the physics literature on disordered solids.

Table 1 Illustration of the different steps of the GASM p0 → P0 → [FT] For each z point: P0 → P1 → [rotation kernel] P1 → p1 z) → [IFT] Compute βp12 → [βp12 kernel] βp12 → F (βp12) → [FT] Rotate F (βp12) → [rotation kernel] Compute integral I → [integral kernel] I → P2 → [rotation kernel] P2 → p2 z) → [IFT] The different FTs, IFTs, and kernels are represented in square brackets.