A wavelets story from the Arctic II
The first book you read in the wavelets field is Ingrid Daubechies book : Ten lectures about wavelets. But this book is mainly for signal theory and a whole book just about the method to construct the wavelets basis. So it was not particularly well suited for our purposes at ctcc solving many body Schr?dinger type equations since the Daubechies wavelets have: 1) Overlapping support 2) they approach a fractal , nowhere differentiable curve for small scales . So when I gave my first intro to you guys at ctcc, I guess I told you that we will concentrate on Alpert's multiwavelets. which also had one nondifferentibale point at the midpoint ,but were both non overlapping and piecewise diffrentiable and also were used on finite number of collocation , interpolation points.
The Abel committee preferred to give the price to Meyer since I assume :1)He coined the term ondelelette or wavelets in 1985-6 before anyone and before Ingrid Daubechesi came out with her works using the same type of concept. 2) In addition to this he wrote two big hard math books about wavelets where he put these into their right approximative Besov spaces wrt nonlinear adaptive truncations and also put truncated Calderon-Zygmund singular operators in the same type of input/output spaces . The last theme I guess was condensed in the so called T(1) theorem specifying this truncation on the identity functional on these spaces. The last theme was also the major theme in the thesis on Newton potential on surfaces for Poisson Greens functions by one of the most brilliant math students from Troms? : ?yvind ?yvind Jacobsen Bj?rk?s with Str?mberg as advisor and me as coadvisor.. He was btw also a silver medalist in the international Chemical Olympiad.
But the story does not stop here since I indeed was in Berkeley in 1989-90 and heard Daubechies give her excellent talk about wavelets which sort of gave me the input to my interest in the field. But the most extraordinary thing happened during the talk, to me at least , was that she gave the honor of who discovered the wavelets not to Meyer who I knew had coined the term wavelets a few years before . but to some guy called Stromberg who discovered totally unnoticed these orthogonal functions already in 1980, 5 years before Meyer did his work. His mistake was perhaps that de did not make a catchy name for his functions since he called them atoms , but still the same thing mathematically. It took some time before during this lecture, I realize that this person she was talking about was my friend and colleague with the name : Jan Olov Str?mberg sititng in the office next to me in the math department at UiT in Troms?. All considered , I believe Meyer gave the largest contribution to math, but the first discoverer of orthogonal wavelets functions was in Troms? at UiT for more than 10 years I guess. . Couldn't you Curt Rice or rather you Morten D?hlen whisper to the leader of the Abel committee that it would be a good idea to give Str?mberg the applause he deserves at this ceremony and priority of being the first man on this planet to think about wavelets functions. He can of course check it out with Meyer first and see what he thinks about it? Without Str?mberg as me and my brother's , Lars Fl?'s teacher since I also started following his seminars when I came back in 1990, I really doubt that our multiwavelets project at ctcc in Troms? could have even started??
PhD(Wavelets).MS.BE.(ME,EE), Owner CRD P/L, Father of the Australian Worsted Comb Fibre processing Technology
7 年I reflect on this again "His mistake was perhaps that he did not make a catchy name for his functions ..." my experience with CSIRO and my work - nothing unusual. I was late comer to Wavelets ( Ondelelette ) - 1996 as part of my PhD. Using Haar to construct complex orthogonal shapes. A year before that Dr.Kiby and I were made redundant by CSIRO. I made similar mistake in CSIRO making "management of science" pretend scientist judgmental on my work and hence make the decision to cut our positions. That was 20y ago. Most notable was need to make functions orthogonal - but with computing power today once can do without that requirement if Wavelet is a "Shape function" constructed to reflect geometric shape - ie reflection from a "stealth " plane is a practical example ...but I am sure there are many in which a generalized shape can be made into a Wavelet .
Managing Director at RadPlanet Friendly Industries Ltd (UK) Non Executive Director at HVPS Holdings Pty Ltd
7 年Dr.Nick.Sokolov CRD, fyi
Biophysics Technology Transfer - Central Nervous System (EEG) Thermodynamics
7 年Hello Tor Fla, thank you for this fine lesson in life.