Sentence examples for complex-valued function on from inspiring English sources

Let be the Banach space of bounded continuous complex-valued function on with the supremum norm.

If f is a complex-valued function on M, define (L g) f:= x mapsto f(g^{-1} cdot x)).

Let (V:,{mathfrak {H}}mapsto {mathfrak {H}}) be the operator of multiplication by a bounded complex-valued function on ({mathbb {Z}}_+).

Since Fourier transforms of all maps in (mathcal {E}_{varLambda}) are supported on a circle, we may see a function in any of the (mathcal{E}_{varLambda}) as a complex-valued function on the unit circle; but the G-action depends on Λ.

Let (psi:[0,1]rightarrow[0,infty)) be a function. If f is a measurable complex-valued function on (mathbb{R}^{n}), then H_{psi}f(x):= int_{0}^{1}f(tx psi(t),dt,quad xin mathbb{R}^{n}. Sometimes (H_{psi}) is called the generalized Hardy operator [5].

This is a complex-valued function on (mathbb{D}); note that as z draws close to b, (langle z,b rangle) goes to infinity, so (e_{omega,b} z)) grows exponentially; on the other hand it decreases exponentially as z draws close to −b.

Theorem 3.7 Let Ω be a domain in C 4 ≅ O, which is a pseudoconvex domain with respect to the complex variables z 1, z 2, z 3, z 4 ¯ and let J 1 ( z ) = g 1 ( z ) + g 3 ( z ) e 4 be a complex-valued function of class C 2 on Ω satisfying the condition of harmonicity (4).

Since is real, the frequency response may be considered a complex-valued function of a real variable.

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

,, are complex numbers, are complex-valued functions on,, and are linear operators in.

(L^{p}(mathbb{R}^{n})) denotes the classical Lebesgue space of complex-valued functions on (mathbb{R}^{n}).