in many ways, #mathematical #physics is based on the #smoothing properties of the #integral

`To prove #boundedness on Lp spaces, Calderón and Zygmund introduced a method of decomposing L1 functions, generalising the rising sun lemma of F. Riesz. This method showed that the operator defined a continuous #operator from L1 to the space of #functions of weak L1. The Marcinkiewicz interpolation theorem and duality then implies that the #singular #integral operator is bounded on all Lp for 1 < p < ∞.`

https://en.wikipedia.org/wiki/Singular_integral_operators_of_convolution_type#General_theory

youtube.com/@xenaproject
for #mathematics #mathsbasics#mathematicallogic #sets #logic #topology #numbertheory #linearalgebra
#probability #measuretheory
#functionalanalysis

Are you keen to read about results in #MathematicalPhysics and Analysis of #PDEs? Take a look at the paper of our previous workshop participant!

#FunctionalAnalysis #SpectralTheory
@univienna

https://arxiv.org/pdf/2303.04527.pdf

We thank Prof Elliott Lieb for taking a long journey from @princeton Princeton
University and giving us an insight into his research work. He is a living example of that the age is only a number and you can still accomplish a lot at the age of 91.
Watch his lecture on YouTube www.youtube.com/@ESIVienna

#MathematicalPhysics #Bosegas #condensedmatter #statisticalmechanics #statmech #functionalanalysis

@univienna

Today in diagrams I liked: This "unit circle" imagination of Lp space for different values of p. Twas a meme that brought me down this Wikipedia rabbit hole but I have been staring at this picture for a very long while now

https://en.m.wikipedia.org/wiki/Lp_space

An example is given of where Euclidean distance falls short: taxi drivers need to use rectilinear distance in gridded cities!

I can read C.
I have never done any C#.
I can write passable C++.
But my expertise is in C*.

Anyone can give me references to study seminorms with unit balls which are convex sets? In particular, the relationship with seminorms with unit balls which are Minkowski sums of said convex sets and their symmetries. What properties can be derived from the original seminorms and so on... Books, papers, anything?
#math #norm #seminorm #minkowski #FunctionalAnalysis

Answering a good question about my #DirichletSeries #FunctionalAnalysis thread from the other day, I actually linked to some references if folks are curious
https://mathstodon.xyz/@meresar_math/109309318624234932