Sentence examples for holomorphic in from inspiring English sources

In other words, the kernel of the operator may fail to be holomorphic in the free variable z ∈ D. To achieve the desired holomorphicity requires that the domain D be pseudo-convex, and two specific forms of this property, strong pseudo-convexity and strong C -linear convexity are discussed in Sect.

Let A(D) be the disc algebra of all continuous complex-valued functions on the unit disc D holomorphic in its interior.

As application, we show that for multi-dimensional affine Itô Lévy processes with state dependent jump part the Fourier transform is holomorphic in a time strip under some stationarity conditions, and give log-affine series representations for the transform.

We compute the Bass stable rank of the algebra A(K sym of real-symmetric functions that are continuous on symmetric compact planar sets K and holomorphic in the interior K∘ of K.

In a rather general setting of Itô Lévy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane.

By "holomorphic Lp-type" we mean that every Lp-spectral multiplier for L is necessarily holomorphic in a complex neighborhood of some point in the L2-spectrum of L. This can only arise if the group algebra L1(G) is non-symmetric.

Let H(D) be the topological vector space of all functions F holomorphic in the unit disc D. We consider the compact convex subset B̃1 = {F ∈ H(D) : F 0) = 0 ∧ |F′ z)| (1 − |z|2) ≤ 1 for z ∈ D} of H(D) and show that G ∈ B̃1 is a support point of B̃1 if and only if Λ G) = {z ∈ D : |G′ z) (1 − |z|2) = 1} ≠ ∅.

Therefore, is holomorphic in the region.

(D zeta )) is holomorphic in (mathfrak {I}zeta >0).

The Dunkl operators enjoy the regularity property: if, the space of holomorphic functions in, then.

However, it is possible that some of these solutions may turn out to be trivial solutions, which occurs when ( λ d ϕ d s ) − 1 ϰ takes on the boundary values of a Q-holomorphic function ψ j on each component of boundary contours Γ j in C 1, α ( C ) which is, moreover, Q-holomorphic in the domain G j bounded by the closed contour Γ j.