Uploaded April 2022 | Updated September 2026, 1 day ago
In this video we prove the Nevanlinna Pick Interpolation Theorem from Complex Analysis and H Infinity Control Theory. This follows the proof found in Garnett's Bounded Analytic Functions using Finite Blanchke Products with a few modifications for clarity.
//Additional Reading
Garnett's "Bounded Analytic Functions" - amzn.to/3KwjE1w
From Vector Spaces to Function Spaces - Yutaka Yamamoto amzn.to/3sU2CVj
Feedback Control Theory - Doyle, Francis, Tannenbaum amzn.to/3HFvuov
//Exercises
//Watch Next
Bode Plots in Neuroscience and Control Theory youtu.be/fVivGKGhbqg
The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XM
Introduction to Control Theory youtu.be/0v4WFmOm764
//Music Provided by Epidemic Sound
All Parts Equal - Airae
Keep Calm - Airae
Alice is on her way - Airae
Dismantle - Peter Sandberg
Video Call from Los Angeles - Trevor Kowalski
Saturday Coffee - William Claeson
Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:
epidemicsound.com/referral/644nao
//Books
Nonlinear Systems - Khalil amzn.to/32Zyk8E
Functions of One Complex Variable - Conway amzn.to/3M0snu6
Real and Complex Analysis - Rudin amzn.to/3riipvZ
Real Analysis - Folland amzn.to/3ogVuiG
Fundamentals of Differential Equations - Nagle, Saff, and Snider amzn.to/3qeGD9C
Advanced Mathematical Analysis - Beals amzn.to/3fn2jdP
From Vector Spaces to Function Spaces - Yutaka Yamamoto amzn.to/3sU2CVj
Feedback Control Theory - Doyle, Francis, Tannenbaum amzn.to/3HFvuov
Pick Interpolation and Hilbert Function Spaces - Agler and McCarthy amzn.to/3EOJU3K
Modern Control Systems - Dorf and Bishop amzn.to/331JQAm
// MATLAB Code
bitbucket.org/joelrosenfeld/nyquist-criterion-video-figures/src/master
//Recording Equipment
Canon SL3: amzn.to/3nZ11KU
Canon T6i: amzn.to/3FUpkQh
Rode VideoMic: amzn.to/3lhldGa
Blue Yeti Microphone: amzn.to/3I1y88N
Yeti Nano Microphone: amzn.to/3I1mriA
SanDisc 256GB SD Card: amzn.to/3E3LOOr
Neewer 5600K USB LED Lights: amzn.to/3xvB9cN
Neewer 18 inch Ring Light: amzn.to/2ZvgCsc
Camera Power Adapter: amzn.to/3D3upUu
DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
0:00 Introduction
0:54 The Period
1:24 Finite Blasche Products
2:42 Base Case
4:09 When all is one
6:22 Who is Georg Alexander Pick?
7:24 Shifting to zero
8:22 Matrix's turn
9:57 An equivalent problem
10:54 Removing a point
13:53 Applications of Pick's Theorem
In this video we prove the Nevanlinna Pick Interpolation Theorem from Complex Analysis and H Infinity Control Theory. This follows the proof found in Garnett's Bounded Analytic Functions using Finite Blanchke Products with a few modifications for clarity.
//Additional Reading
Garnett's "Bounded Analytic Functions" - amzn.to/3KwjE1w
From Vector Spaces to Function Spaces - Yutaka Yamamoto amzn.to/3sU2CVj
Feedback Control Theory - Doyle, Francis, Tannenbaum amzn.to/3HFvuov
//Exercises
//Watch Next
Bode Plots in Neuroscience and Control Theory youtu.be/fVivGKGhbqg
The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XM
Introduction to Control Theory youtu.be/0v4WFmOm764
//Music Provided by Epidemic Sound
All Parts Equal - Airae
Keep Calm - Airae
Alice is on her way - Airae
Dismantle - Peter Sandberg
Video Call from Los Angeles - Trevor Kowalski
Saturday Coffee - William Claeson
Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:
epidemicsound.com/referral/644nao
//Books
Nonlinear Systems - Khalil amzn.to/32Zyk8E
Functions of One Complex Variable - Conway amzn.to/3M0snu6
Real and Complex Analysis - Rudin amzn.to/3riipvZ
Real Analysis - Folland amzn.to/3ogVuiG
Fundamentals of Differential Equations - Nagle, Saff, and Snider amzn.to/3qeGD9C
Advanced Mathematical Analysis - Beals amzn.to/3fn2jdP
From Vector Spaces to Function Spaces - Yutaka Yamamoto amzn.to/3sU2CVj
Feedback Control Theory - Doyle, Francis, Tannenbaum amzn.to/3HFvuov
Pick Interpolation and Hilbert Function Spaces - Agler and McCarthy amzn.to/3EOJU3K
Modern Control Systems - Dorf and Bishop amzn.to/331JQAm
// MATLAB Code
bitbucket.org/joelrosenfeld/nyquist-criterion-video-figures/src/master
//Recording Equipment
Canon SL3: amzn.to/3nZ11KU
Canon T6i: amzn.to/3FUpkQh
Rode VideoMic: amzn.to/3lhldGa
Blue Yeti Microphone: amzn.to/3I1y88N
Yeti Nano Microphone: amzn.to/3I1mriA
SanDisc 256GB SD Card: amzn.to/3E3LOOr
Neewer 5600K USB LED Lights: amzn.to/3xvB9cN
Neewer 18 inch Ring Light: amzn.to/2ZvgCsc
Camera Power Adapter: amzn.to/3D3upUu
DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
0:00 Introduction
0:54 The Period
1:24 Finite Blasche Products
2:42 Base Case
4:09 When all is one
6:22 Who is Georg Alexander Pick?
7:24 Shifting to zero
8:22 Matrix's turn
9:57 An equivalent problem
10:54 Removing a point
13:53 Applications of Pick's Theorem
