Struct BanachSpace 

pub struct BanachSpace {
    pub p: f64,
    pub dx: f64,
}

A discrete Banach space with Lᵖ norm.

Supports p-norms, dual space estimation, and bounded linear functional evaluation.

Fields

p: f64

The exponent p for the Lᵖ norm (p >= 1).

dx: f64

Grid spacing for integration approximation.

Implementations

impl BanachSpace

pub fn new(p: f64, dx: f64) -> Self

Create a new BanachSpace with Lᵖ norm and spacing dx.

pub fn norm(&self, f: &[f64]) -> f64

Compute the Lᵖ norm ‖f‖_p = (∫|f|^p dx)^{1/p}.

pub fn dual_norm(&self, g: &[f64]) -> f64

Compute the dual Lᵍ norm where 1/p + 1/q = 1.

For p = 1 returns the L∞ norm; for p = ∞ returns the L¹ norm.

pub fn bounded_linear_functional(&self, f: &[f64], g: &[f64]) -> f64

Evaluate a bounded linear functional φ(f) = ∫ g(x) f(x) dx.

g is the Riesz representation kernel.

pub fn in_unit_ball(&self, f: &[f64], tol: f64) -> bool

Check whether f lies in the unit ball ‖f‖_p <= 1 + tol.

pub fn holder_bound(&self, f: &[f64], g: &[f64]) -> (f64, f64)

Compute the Hölder bound: |⟨f, g⟩| <= ‖f‖_p * ‖g‖_q.

Returns (lhs, rhs) where lhs = |⟨f,g⟩| and rhs = ‖f‖_p * ‖g‖_q.

Trait Implementations

impl Clone for BanachSpace

fn clone(&self) -> BanachSpace

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for BanachSpace

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.