L2Space: Creates the L2-space for a Reference Measure

In DistributionalDDA: Distributional Data Analysis in Bayes Spaces

Creates the L2-space for a Reference Measure

Description

An L2-space is a Hilbert space of with respect to the reference measure square integrable functions. They are vector addition and multiplication with a scalar is done on the results. The scalar product is defined integrating the product of two functions over the reference measure.

Usage

L2Space(x = StdReferenceMeasureUnif01, ...)

## S3 method for class 'ReferenceMeasure'
L2Space(x, ...)

## S3 method for class 'BayesSpace'
L2Space(x, ...)

Arguments

x	the ReferenceMeasure of the L2 space
...	further arguments for generic use

Value

An object of class '"L2Space"': a list holding the reference measure.

Methods (by class)

• L2Space(ReferenceMeasure): Method for ReferenceMeasure

• L2Space(BayesSpace): Method for BayesSpaces.

See Also

[ReferenceMeasure]

Other BayesSpace: BayesSpace()

Examples

space = L2Space(ReferenceMeasureUniform(0,10))
space
bs = BayesSpace(ReferenceMeasureUniform(0,10))
space2 = L2Space(bs)
space2

DistributionalDDA documentation built on Oct. 20, 2026, 5:06 p.m.