Understanding Sturn-Liouville Theory: Stone-Weierstrass Conditions Explained

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SUMMARY

The discussion centers on the Stone-Weierstrass theorem and its application to infinite dimensional vector spaces, particularly in the context of Sturn-Liouville theory. Participants emphasize the importance of understanding linear independence and generating sets in infinite dimensions. The Stone-Weierstrass conditions are confirmed to be applicable, providing a foundation for further exploration of these mathematical concepts. The discussion highlights the necessity of grasping these principles for solving related problems in functional analysis.

PREREQUISITES
  • Understanding of the Stone-Weierstrass theorem
  • Familiarity with infinite dimensional vector spaces
  • Knowledge of linear independence and generating sets
  • Basic concepts of functional analysis
NEXT STEPS
  • Study the implications of the Stone-Weierstrass theorem in functional analysis
  • Explore the properties of infinite dimensional vector spaces
  • Learn about linear independence in the context of infinite dimensions
  • Investigate applications of Sturn-Liouville theory in differential equations
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Mathematicians, physicists, and students studying functional analysis or differential equations, particularly those interested in the applications of the Stone-Weierstrass theorem and Sturn-Liouville theory.

mplltt
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https://www.physicsforums.com/attachments/7087https://www.physicsforums.com/attachments/7091The same conditions from Stone-Weierstrass apply.
 
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Sorry about the links

This is the Stone-Weierstrass I was talking about.

https://www.physicsforums.com/attachments/7094

Please! I must solve this problem:

https://www.physicsforums.com/attachments/7095

Thanks for the help
-M
 
Last edited:
What does it mean for an infinite dimensional vector space to have a basis? How do the notions of linear independence and a generating set translate into the infinite dimensional setting?
 

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