Invidious

MIT 18.102 Introduction to Functional Analysis, Spring 2021

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MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: ocw.mit.edu/courses/18-102-introduction-to-functio… Functional analysis helps us study and solve both linear and nonlinear problems posed on a normed space that is no longer finite-dimensional, a situation that arises very naturally in many concrete problems. Topics include normed spaces, completeness, functionals, the Hahn-Banach Theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of Lᵖ spaces; Hilbert spaces; compact and self-adjoint operators; and the Spectral Theorem. License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms More courses at ocw.mit.edu Support OCW at ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at ocw.mit.edu/comments.

1:15:19

Lecture 1: Basic Banach Space Theory

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1:24:11

Lecture 2: Bounded Linear Operators

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1:04:02

Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem

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1:14:58

Lecture 4: The Open Mapping Theorem and the Closed Graph Theorem

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1:10:24

Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem

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1:20:58

Lecture 6: The Double Dual and the Outer Measure of a Subset of Real Numbers

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1:20:24

Lecture 7: Sigma Algebras

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1:14:02

Lecture 8: Lebesgue Measurable Subsets and Measure

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1:24:57

Lecture 9: Lebesgue Measurable Functions

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1:22:55

Lecture 10: Simple Functions

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1:21:38

Lecture 11: The Lebesgue Integral of a Nonnegative Function and Convergence Theorems

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1:24:57

Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence...

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1:23:59

Lecture 13: Lp Space Theory

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1:23:24

Lecture 14: Basic Hilbert Space Theory

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1:16:02

Lecture 15: Orthonormal Bases and Fourier Series

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1:21:23

Lecture 16: Fejer’s Theorem and Convergence of Fourier Series

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1:16:04

Lecture 17: Minimizers, Orthogonal Complements and the Riesz Representation Theorem

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1:12:18

Lecture 18: The Adjoint of a Bounded Linear Operator on a Hilbert Space

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1:23:23

Lecture 19: Compact Subsets of a Hilbert Space and Finite-Rank Operators

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1:22:25

Lecture 20: Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space

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1:10:51

Lecture 21: The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint...

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1:24:07

Lecture 22: The Spectral Theorem for a Compact Self-Adjoint Operator

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1:23:54

Lecture 23: The Dirichlet Problem on an Interval

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