45:55A Simple Consequence of Morera's Theorem and the Hilbert Hardy space.
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A 46-minute video from AMAT 611: Functional Analysis - Basic Principles: “A Simple Consequence of Morera's Theorem and the Hilbert Hardy space.”.
AMAT 611: Functional Analysis - Basic Principles
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45:55
1:10:27Adjoints of Hilbert space Operators
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A 70-minute video from AMAT 611: Functional Analysis - Basic Principles: “Adjoints of Hilbert space Operators”.
1:23:29Applications of the Hahn Banach Theorem Part I
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A 83-minute video from AMAT 611: Functional Analysis - Basic Principles: “Applications of the Hahn Banach Theorem Part I”.
1:38:54Banach Alaoglu theorem, Reflexive Banach spaces, and Applications
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A 99-minute video from AMAT 611: Functional Analysis - Basic Principles: “Banach Alaoglu theorem, Reflexive Banach spaces, and Applications”.
50:21Basics of Bounded Linear Operators and Examples
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A 50-minute video from AMAT 611: Functional Analysis - Basic Principles: “Basics of Bounded Linear Operators and Examples”.
57:10Basics of Hilbert Spaces and the Nearest Point Theorem
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A 57-minute video from AMAT 611: Functional Analysis - Basic Principles: “Basics of Hilbert Spaces and the Nearest Point Theorem”.
40:27Bounded Linear Functionals and the Riesz Representation Theorem
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A 40-minute video from AMAT 611: Functional Analysis - Basic Principles: “Bounded Linear Functionals and the Riesz Representation Theorem”.
1:29:19Closed Graph Theorem and Quotient Spaces
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A 89-minute video from AMAT 611: Functional Analysis - Basic Principles: “Closed Graph Theorem and Quotient Spaces”.
47:47Competions of Normed Vector Spaces Part II
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A 48-minute video from AMAT 611: Functional Analysis - Basic Principles: “Competions of Normed Vector Spaces Part II”.
35:16Completeness of Lp
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A 35-minute video from AMAT 611: Functional Analysis - Basic Principles: “Completeness of Lp”.
47:16Completions of Normed Vector Spaces Part I
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A 47-minute video from AMAT 611: Functional Analysis - Basic Principles: “Completions of Normed Vector Spaces Part I”.
1:33:06Finite Dimensional Normed Spaces and Compact Operators
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A 93-minute video from AMAT 611: Functional Analysis - Basic Principles: “Finite Dimensional Normed Spaces and Compact Operators”.
1:44:15Finite rank operators, Hilbert Schmidt operators, and Eigenvalues of Compact Operators
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A 104-minute video from AMAT 611: Functional Analysis - Basic Principles: “Finite rank operators, Hilbert Schmidt operators, and Eigenvalues of Compact Operators”.
1:13:20Fredholm Alternative
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A 73-minute video from AMAT 611: Functional Analysis - Basic Principles: “Fredholm Alternative”.
51:36Introduction to Banach spaces
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A 52-minute video from AMAT 611: Functional Analysis - Basic Principles: “Introduction to Banach spaces”.
40:24Introduction to Normed Vector Spaces
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A 40-minute video from AMAT 611: Functional Analysis - Basic Principles: “Introduction to Normed Vector Spaces”.
53:10Matrix of an operator and Hermitian operators
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A 53-minute video from AMAT 611: Functional Analysis - Basic Principles: “Matrix of an operator and Hermitian operators”.
1:10:16Open Mapping Theorem
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A 70-minute video from AMAT 611: Functional Analysis - Basic Principles: “Open Mapping Theorem”.
53:11Orthonormal Bases of Hilbert Spaces Part II: Fourier series, the Bergman space, and RKHS.
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A 53-minute video from AMAT 611: Functional Analysis - Basic Principles: “Orthonormal Bases of Hilbert Spaces Part II: Fourier series, the Bergman space, and RKHS.”.
1:01:27Orthonormal Bases of Hilbert Spaces Part I
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A 61-minute video from AMAT 611: Functional Analysis - Basic Principles: “Orthonormal Bases of Hilbert Spaces Part I”.
1:15:17Principle of Uniform Boundedness and Applications
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A 75-minute video from AMAT 611: Functional Analysis - Basic Principles: “Principle of Uniform Boundedness and Applications”.
49:59Proof of the Spectral Theorem for Compact Normal Operators, continued
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A 50-minute video from AMAT 611: Functional Analysis - Basic Principles: “Proof of the Spectral Theorem for Compact Normal Operators, continued”.
37:49Reproducing Kernel Hilbert Spaces and Orthogonal Projections
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A 38-minute video from AMAT 611: Functional Analysis - Basic Principles: “Reproducing Kernel Hilbert Spaces and Orthogonal Projections”.
50:02Sobolev Spaces and Weak Solutions of Differential Equations
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A 50-minute video from AMAT 611: Functional Analysis - Basic Principles: “Sobolev Spaces and Weak Solutions of Differential Equations”.
1:22:49Spectral Theorem of Compact Normal Operators
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A 83-minute video from AMAT 611: Functional Analysis - Basic Principles: “Spectral Theorem of Compact Normal Operators”.
56:23The Projection Theorem for Hilbert Spaces
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A 56-minute video from AMAT 611: Functional Analysis - Basic Principles: “The Projection Theorem for Hilbert Spaces”.
42:38Triangle Inequality for lp
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A 43-minute video from AMAT 611: Functional Analysis - Basic Principles: “Triangle Inequality for lp”.
1:23:39Unitary operators, unitary equivalence, and applications to discrete convolution
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A 84-minute video from AMAT 611: Functional Analysis - Basic Principles: “Unitary operators, unitary equivalence, and applications to discrete convolution”.
1:37:48Zorn's Lemma and Hahn Banach Theorem
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A 98-minute video from AMAT 611: Functional Analysis - Basic Principles: “Zorn's Lemma and Hahn Banach Theorem”.