complex valued
Alternative names
complex-valued
Examples
An example of a rapidly falling function is for any positive n, λ, β. To study the Fourier transform, it is best to consider complex-valued test functions and complex-linear distributions.
If we use complex-valued functions, the space L ∞ is a commutative C*-algebra with pointwise multiplication and conjugation.
Series of functions main A series of real- or complex-valued functions : converges pointwise on a set E, if the series converges for each x in E as an ordinary series of real or complex numbers.
In other words, if u and v are real-differentiable functions of two real variables, obviously u + iv is a (complex-valued) real-differentiable function, but u + iv is complex-differentiable if and only if the Cauchy–Riemann equations hold.
It has also been used to refer to only the real component ε' r of the complex-valued relative permittivity.
It has the advantage of working also for complex-valued random variables or for random variables taking values in any measurable space (which includes topological spaces endowed by appropriate σ-algebras).