HilbertRxToSupremumRdFinite

java.lang.Object

org.drip.spaces.functionclass.NormedRxToNormedRxFinite

org.drip.spaces.functionclass.NormedRxToNormedRdFinite

org.drip.spaces.functionclass.HilbertRxToSupremumRdFinite

public class HilbertRxToSupremumRdFinite
extends NormedRxToNormedRdFinite

HilbertRxToSupremumRdFinite implements the Class F with f E f : Hilbert R^x To Supremum R^d Space of Finite Functions. The References are:

Carl, B. (1985): Inequalities of the Bernstein-Jackson type and the Degree of Compactness of Operators in Banach Spaces Annals of the Fourier Institute 35 (3) 79-118
Carl, B., and I. Stephani (1990): Entropy, Compactness, and the Approximation of Operators Cambridge University Press Cambridge UK
Williamson, R. C., A. J. Smola, and B. Scholkopf (2000): Entropy Numbers of Linear Function Classes, in: Proceedings of the 13th Annual Conference on Computational Learning Theory ACM New York

It provides the following Functionality:

HilbertRxToSupremumRdFinite Constructor

Module	Computational Core Module
Library	Statistical Learning Library
Project	R¹ and R^d Vector/Tensor Spaces (Validated and/or Normed), and Function Classes
Package	Normed Finite Spaces Function Class

Author:: Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor Description

HilbertRxToSupremumRdFinite(double maureyConstant, NormedRxToNormedRd[] hilbertRxToSupremumRdArray)
HilbertRxToSupremumRdFinite Constructor
Method Summary

Methods inherited from class org.drip.spaces.functionclass.NormedRxToNormedRdFinite
agnosticCoveringNumberBounds, functionSpaces, inputMetricVectorSpace, operatorPopulationMetricNorm, operatorPopulationSupremumNorm, operatorSampleMetricNorm, operatorSampleSupremumNorm, outputMetricVectorSpace, populationCoveringNumber, populationCoveringNumber, populationRdMetricNorm, populationRdSupremumNorm, populationSupremumCoveringNumber, populationSupremumCoveringNumber, sampleCoveringNumber, sampleCoveringNumber, sampleRdMetricNorm, sampleRdSupremumNorm, sampleSupremumCoveringNumber, sampleSupremumCoveringNumber

Methods inherited from class org.drip.spaces.functionclass.NormedRxToNormedRxFinite
maureyConstant, outputDimension, populationMetricCoveringBounds, populationSupremumCoveringBounds, sampleMetricCoveringBounds, sampleSupremumCoveringBounds, scaleSensitiveCoveringBounds

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details
- HilbertRxToSupremumRdFinite
  
  public HilbertRxToSupremumRdFinite(double maureyConstant, NormedRxToNormedRd[] hilbertRxToSupremumRdArray) throws java.lang.Exception
  
  HilbertRxToSupremumRdFinite Constructor
  
  Parameters:
  
  maureyConstant - Maurey Constant
  
  hilbertRxToSupremumRdArray - Array of the Hilbert R^x To Supremum R^d Spaces
  
  Throws:
  
  java.lang.Exception - Thrown if the Inputs are Invalid