Namespaces
Variants
Actions

Difference between revisions of "Talk:Arveson spectrum"

From Encyclopedia of Mathematics
Jump to: navigation, search
(translation: forward or backward?)
Line 1: Line 1:
A rapid check shows that $\hat{x}(n)$ does not exactly satisfy the indicated equation but rather with an inverse
+
1. A rapid check shows that $\hat{x}(n)$ does not exactly satisfy the indicated equation but rather with an inverse
 
$$U_z \hat{x}(n) = (z)^{-1} \hat{x}(n)$$
 
$$U_z \hat{x}(n) = (z)^{-1} \hat{x}(n)$$
 
Even if there is no ambiguity, it would also be better if we make it clear that $\hat{x}(n)$ is still a function on $T$ (while usually in Fourier transform, the transform is a function on the "Fourier space" which I admit is just a word that doesn't explain anything)
 
Even if there is no ambiguity, it would also be better if we make it clear that $\hat{x}(n)$ is still a function on $T$ (while usually in Fourier transform, the transform is a function on the "Fourier space" which I admit is just a word that doesn't explain anything)
# A question: "vector-valued Riemann integral", is that the same thing as Bochner integrals?
+
 
 +
2. A question: "vector-valued Riemann integral", is that the same thing as Bochner integrals?
 +
 
 +
: 1. I guess the result depends on the interpretation of the phrase "take translation for $\{U_z\}$". What is meant by the translation by $z$ of a function $x$? Is it the function $w \mapsto x(zw)$ or $w \mapsto x(z^{-1}w)$? [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 13:10, 15 May 2014 (CEST)

Revision as of 11:10, 15 May 2014

1. A rapid check shows that $\hat{x}(n)$ does not exactly satisfy the indicated equation but rather with an inverse $$U_z \hat{x}(n) = (z)^{-1} \hat{x}(n)$$ Even if there is no ambiguity, it would also be better if we make it clear that $\hat{x}(n)$ is still a function on $T$ (while usually in Fourier transform, the transform is a function on the "Fourier space" which I admit is just a word that doesn't explain anything)

2. A question: "vector-valued Riemann integral", is that the same thing as Bochner integrals?

1. I guess the result depends on the interpretation of the phrase "take translation for $\{U_z\}$". What is meant by the translation by $z$ of a function $x$? Is it the function $w \mapsto x(zw)$ or $w \mapsto x(z^{-1}w)$? Boris Tsirelson (talk) 13:10, 15 May 2014 (CEST)
How to Cite This Entry:
Arveson spectrum. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Arveson_spectrum&oldid=32161