Uploaded May 2022 | Updated September 2026, 1 day ago
In this video we look at the most important operator in all of operator theory, and this operator is the multiplication operator. We look at multiplication operators over reproducing kernel Hilbert Spaces, and we examine a connection with the Nevanlinna Pick Interpolation Theorem.
//Additional Reading
Agler and McCarthy's "Pick Interpolation and Hilbert Function Spaces" - amzn.to/3wcoxXW
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 and the Model Matching Problem youtu.be/fVivGKGhbqg
The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XM
Nevanlinna - Pick Interpolation Theorem youtu.be/UhSv5iWOtA4
The Real Analysis Survival Guide youtu.be/v5rD0B-zfXw
Introduction to Control Theory youtu.be/0v4WFmOm764
//Music Provided by Epidemic Sound
Place Called Home - Jones Meadow
Like a Blind Girl's Dog - Daxten
Alice is on Her Way - Aerai
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
//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
1:00 Multiplication Operators and Kernel Spaces
2:35 Bounding the Function
4:11 The Hardy Space of the Disc
5:45 Bounding the Operator
7:58 Multiplication Operators and the Nevanlinna Pick Theorem
In this video we look at the most important operator in all of operator theory, and this operator is the multiplication operator. We look at multiplication operators over reproducing kernel Hilbert Spaces, and we examine a connection with the Nevanlinna Pick Interpolation Theorem.
//Additional Reading
Agler and McCarthy's "Pick Interpolation and Hilbert Function Spaces" - amzn.to/3wcoxXW
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 and the Model Matching Problem youtu.be/fVivGKGhbqg
The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XM
Nevanlinna - Pick Interpolation Theorem youtu.be/UhSv5iWOtA4
The Real Analysis Survival Guide youtu.be/v5rD0B-zfXw
Introduction to Control Theory youtu.be/0v4WFmOm764
//Music Provided by Epidemic Sound
Place Called Home - Jones Meadow
Like a Blind Girl's Dog - Daxten
Alice is on Her Way - Aerai
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
//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
1:00 Multiplication Operators and Kernel Spaces
2:35 Bounding the Function
4:11 The Hardy Space of the Disc
5:45 Bounding the Operator
7:58 Multiplication Operators and the Nevanlinna Pick Theorem
