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#Analytic Function Spaces

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Fields Institute

Sarason's Ha-plitz Product Problem

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Explore Sarason's Ha-plitz product problem, its implications in analytic function spaces, and recent developments in this challenging mathematical area.
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12 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

Hardy Spaces: Uniqueness and Harmonic Representation Theorems - Part 6

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Explore uniqueness, harmonic representation, and representation theorems in Hardy spaces, advancing understanding of analytic function spaces and their applications.
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5 Lesons
50 minutes
On-Demand
Free-Video
Fields Institute

Mini-course on Hardy Spaces - Part 3

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Explore Hardy spaces with a focus on rotation, generalization, and approximate identities. Delve into uniform boundedness, Poisson PR constructions, and harmonic functions.
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11 Lesons
57 minutes
On-Demand
Free-Video
Fields Institute

Quotients of the Drury-Arveson Space and Their Classification in Terms of Complex Geometry

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Explore quotients of Drury-Arveson space, their classification using complex geometry, and connections to hyperbolic metrics and holomorphic multipliers in this advanced mathematical lecture.
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16 Lesons
57 minutes
On-Demand
Free-Video
Fields Institute

Gelfand Transformations and Boundary Representations of Complete Nevanlinna-Pick Quotients

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Explore Gelfand transformations and boundary representations in Nevanlinna-Pick quotients, covering univariate settings, approximation sets, and isolated points in boundary representations.
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7 Lesons
25 minutes
On-Demand
Free-Video
Fields Institute

Commutant Lifting and Nevanlinna-Pick Interpolation in Several Variables

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Explore advanced topics in complex analysis, including commutant lifting and Nevanlinna-Pick interpolation across multiple variables, with applications in function spaces and operator theory.
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15 Lesons
47 minutes
On-Demand
Free-Video
Fields Institute

Mini-Course on Non-Commutative Function Theory - Part 2

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Explore non-commutative function theory, covering square summable series, homogeneous sums, and the Rhoda string theorem in this advanced mathematical lecture.
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8 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Two Weight Norm Inequalities for Singular and Fractional Integral Operators in Rn

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Explore singular and fractional integral operators in Rn, focusing on two weight norm inequalities. Learn about A2 and AP weights, pivotal conditions, and cancellation properties.
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23 Lesons
58 minutes
On-Demand
Free-Video
Fields Institute

Sums of Squares and Applications to Hypoellipticity

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Explore sums of squares in differential equations, focusing on hypoellipticity. Learn about key theorems, counterexamples, and applications in this advanced mathematics lecture.
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13 Lesons
48 minutes
On-Demand
Free-Video
Fields Institute

Generators of C0-Semigroups of Weighted Composition Operators

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Explore generators of C0-semigroups and weighted composition operators in analytic function spaces, examining key assumptions, proofs, and recent developments in the field.
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14 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Totally Positive Kernels, Polya Frequency Functions, and Their Transforms

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Explore total positivity in mathematics, including real-rooted polynomials, composition operators, and Hankel kernels. Gain insights into preservers of TN kernels and TP kernel approximations.
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18 Lesons
51 minutes
On-Demand
Free-Video
Fields Institute

BMO and Variations

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Explore rearrangement, continuity, and improved constants in BMO variations. Gain insights into uniform domains and local BMO extensions in this advanced mathematical analysis.
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13 Lesons
55 minutes
On-Demand
Free-Video
Fields Institute

Measures with L2-Bounded Riesz Transform and the Painlevé Problem for Lipschitz Harmonic Functions

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Explore uniform rectifiability, curvature of measures, and removability in relation to Lipschitz harmonic functions and the Painlevé problem in this advanced mathematics lecture.
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14 Lesons
55 minutes
On-Demand
Free-Video
Fields Institute

Colloquium Talk on Interpolation and Sampling

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Explore interpolation and sampling in analytic function spaces, covering historical context, general problems, and modern perspectives on this mathematical topic.
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12 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

The Invariant Subspace Problem: A Brief Overview of Recent Developments

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Explore recent developments in the invariant subspace problem, covering history, proofs, reflexivity, and various techniques in operator theory and functional analysis.
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15 Lesons
55 minutes
On-Demand
Free-Video
Fields Institute

Mini-course on Interpolation and Sampling - Part 2

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Explore advanced concepts in interpolation and sampling, including Hardy spaces, Carleson measures, and weak interpolation in analytic function theory.
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10 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

Conjugations in L2 Spaces on the Unit Circle and the Real Line

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Explore conjugations in L2 spaces, examining various types and their applications on the unit circle and real line. Includes examples and connections to Fourier transforms.
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12 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Model Spaces in Analytic Function Theory - Part 1

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Explore model spaces in function theory, covering key concepts like reproducing kernels and inner function spectra. Gain insights into both finite and infinite dimensional cases.
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10 Lesons
54 minutes
On-Demand
Free-Video
Fields Institute

Three Problems on Univalent Functions in Model Spaces

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Explore univalent functions in model spaces, covering new linear domains, observed continuation, and characterization theorems. Gain insights into complex analysis and function theory.
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10 Lesons
54 minutes
On-Demand
Free-Video
Fields Institute

Hilbert Matrix Operator on Bergman-Type Spaces

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Explore the Hilbert matrix operator's behavior on various analytic function spaces, including Hardy, Bergman, and Besov spaces, with applications in complex analysis.
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11 Lesons
54 minutes
On-Demand
Free-Video
Fields Institute

Polynomial Approximation of Inverses of Functions in Dirichlet-Type Spaces

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Explores polynomial approximation of function inverses in Dirichlet-type spaces, covering optimal approximants, cyclicity, and convergence. Discusses challenges and open questions in the field.
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12 Lesons
49 minutes
On-Demand
Free-Video
Fields Institute

Approximation and Closed Ideals in Some Analytic Spaces

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Explore approximation theory and closed ideals in analytic spaces, focusing on key theorems, inequalities, and applications in functional analysis.
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5 Lesons
29 minutes
On-Demand
Free-Video
Fields Institute

Blaschke Products and the Crouzeix Conjecture

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Explore Blaschke products and their connection to the Crouzeix conjecture in complex analysis, examining numerical ranges, model spaces, and level sets in operator theory.
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18 Lesons
48 minutes
On-Demand
Free-Video
Fields Institute

Describing Blaschke Products by Their Critical Points

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Explore critical points in Blaschke products, inner functions, and related theorems. Gain insights into analytic function spaces and their applications in complex analysis.
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13 Lesons
1 hour
On-Demand
Free-Video
Fields Institute

Mini-course on Blaschke Products and Inner Functions - Part 1

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Explore Blaschke products and inner functions in complex analysis, covering definitions, singular inner functions, and dynamical properties in this advanced mathematics lecture.
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7 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

Contractive Inequalities for Hardy Spaces

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Explore contractive inequalities in Hardy spaces, covering Henson's inequality, hyperspace, critical exponents, and geometric problems in analytic function theory.
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16 Lesons
56 minutes
On-Demand
Free-Video
Fields Institute

Studying Wave Operators Using Complex Analysis - Some One-Dimensional and Multidimensional Results

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Explore wave operators through complex analysis, examining one-dimensional and multidimensional results for advanced mathematical insights and applications.
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1 Lesons
51 minutes
On-Demand
Free-Video
Fields Institute

The Non-Commutative Analytic Toeplitz Algebra and Free Semigroup Algebras

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Explore non-commutative analytic Toeplitz algebra and free semigroup algebras, covering topics like weak operator topology, functional calculus, and invariant subspaces.
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19 Lesons
54 minutes
On-Demand
Free-Video
Fields Institute

Mini-course on Non-Commutative Function Theory - Part 1

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Explore non-commutative function theory fundamentals in this concise lecture, covering key concepts and applications in advanced mathematical analysis.
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1 Lesons
54 minutes
On-Demand
Free-Video
Fields Institute

Backward Maps Have Gone Nuclear - Factorization Theorems of Backward Shifts and Nuclear Maps

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Explore factorization theorems of backward shifts and nuclear maps, delving into advanced mathematical concepts and their applications in analytic function spaces.
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1 Lesons
55 minutes
On-Demand
Free-Video
Fields Institute

Absolutely Summing Composition Operators on Bloch Spaces

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Explore composition operators on Bloch spaces, focusing on boundedness, compactness, and absolutely summing properties. Includes examples like lens and cusp maps.
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13 Lesons
50 minutes
On-Demand
Free-Video
Fields Institute

Blaschke Products and Inner Functions - Part 3

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Explore advanced concepts in complex analysis, focusing on Blaschke products and inner functions in this in-depth mathematical lecture by Artur Nicolau.
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1 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Shift Invariant Subspaces of Composition Operators

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Explore shift invariant subspaces of composition operators in analytic function spaces, focusing on their properties and applications in mathematical analysis.
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1 Lesons
22 minutes
On-Demand
Free-Video
Fields Institute

On the Spectrum of the Hilbert Matrix

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Explore the intriguing properties and spectral analysis of the Hilbert matrix in this advanced mathematical lecture by Dragan Vukotic from Universidad Autónoma de Madrid.
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1 Lesons
56 minutes
On-Demand
Free-Video
Fields Institute

Mini-Course on Truncated Toeplitz Operators - Part 1

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Explore truncated toeplitz operators in this comprehensive lecture by Emmanuel Fricain, delving into advanced mathematical concepts and their applications in analytic function spaces.
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1 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

High-Energy Behaviour of Weyl Coefficients

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Explore the high-energy behavior of Weyl coefficients in analytic function spaces, presented by Harald Woracek from Vienna University of Technology.
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1 Lesons
51 minutes
On-Demand
Free-Video
Fields Institute

Smooth Functions in Extreme de Branges-Rovnyak Spaces

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Explore extreme de Branges-Rovnyak spaces and their smooth functions in this advanced mathematical analysis, focusing on analytic function spaces and their applications.
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1 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

Mini-Course on Interpolation & Sampling Part 1

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Explore fundamental concepts of interpolation and sampling in analytic function spaces with expert Andreas Hartmann from the University of Bordeaux.
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1 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

Hyperbolic Fourier Series

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Explore advanced mathematical concepts in hyperbolic Fourier series, delving into complex analysis and function spaces with expert insights from Håkan Hedenmalm.
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1 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

A Decomposition of Analytic Function Spaces, With Applications

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Explore analytic function spaces decomposition and its applications in this insightful lecture by Jonathan Partington from the University of Leeds.
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1 Lesons
51 minutes
On-Demand
Free-Video
Fields Institute

Hardy Spaces Mini-Course and Workshop - Part 5

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Explore advanced concepts in Hardy spaces, focusing on analytic function theory and its applications in complex analysis and functional analysis.
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1 Lesons
59 minutes
On-Demand
Free-Video
Fields Institute

Hardy Spaces Mini-Course and Workshop - Part 4

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Explore advanced concepts in Hardy spaces, focusing on analytic function theory and its applications in complex analysis and functional analysis.
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1 Lesons
46 minutes
On-Demand
Free-Video