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Apr
9
revised Analogs of the paralleloram identity in higher degrees
formula
Apr
9
comment Analogs of the paralleloram identity in higher degrees
Yes... differentiation can be defined inductively on polynomials... Qiaochu, anyway this formula (of polarization) is absurd, I don't like it. What is it called when a variable is not free and at the same time not bound in a formula? It seems to me I saw an explanation somewhere that this is not good...
Apr
9
revised Analogs of the paralleloram identity in higher degrees
grammar
Apr
9
comment What are the analogs of quadratic forms of degree $k>2$?
OK, I posted this as another question: math.stackexchange.com/questions/1226024/…
Apr
8
asked Analogs of the paralleloram identity in higher degrees
Apr
8
accepted What are the analogs of quadratic forms of degree $k>2$?
Apr
4
comment What are the analogs of quadratic forms of degree $k>2$?
Qiaochu, I feel like a student with you. How does this polarization define "parallelogram identity", say, for cubic forms?
Apr
4
comment What are the analogs of quadratic forms of degree $k>2$?
What I don't understand in this science: if quadratic forms have analogs in higher degrees, then there must be analogs of parallelogram identity for cubic forms, quartic froms, etc. What are they?
Apr
3
comment What are the analogs of quadratic forms of degree $k>2$?
It will take me some time to find this book...
Apr
3
comment What are the analogs of quadratic forms of degree $k>2$?
I need a reference... It's not good to invent a bicycle...
Apr
3
comment What are the analogs of quadratic forms of degree $k>2$?
Qiaochu, I think it's not good to refer to books on jet bundles when mentioning these elementary facts. Do you know a textbook on algebra where this bijection between homogenious polynomials and symmetric multilinear forms is described?
Apr
3
comment What are the analogs of quadratic forms of degree $k>2$?
"Algebraic form of degree $k$"?
Apr
3
revised What are the analogs of quadratic forms of degree $k>2$?
edited title
Apr
3
comment What are the analogs of quadratic forms of degree $k>2$?
@Shalop, for $k=2$ there is a theory that establishes a bijection between quadratic forms and symmetric bilinear forms. What is this theory for $k>2$? I even can't find any mentionings of these analogs of quadratic forms.
Apr
3
asked What are the analogs of quadratic forms of degree $k>2$?
Feb
25
comment Irreducible representations of $C(T,B(X))$
Thak you! Of course, I had in mind the unitary equivalence of representations!
Feb
25
accepted Irreducible representations of $C(T,B(X))$
Feb
23
asked Irreducible representations of $C(T,B(X))$
Jan
25
comment Is a matrix element of a norm continuous representation always a trigonometric polynomial?
A trivial example: let $\sigma:G\to B(H)$ be a unitary irreducible representation, and $H^{\mathbb N}$ be the countable "Hilbert power of $H$". Then $\pi(t)(x_1,x_2,...)=(\sigma(t)x_1,\sigma(t)x_2,...)$ is a norm continuous irreducible representation of $G$. Shtern says that if we vary the power of $H$ (i.e. take different cardinal numbers instead of ${\mathbb N}$) and add a finite set of similar Hilbert powers, this will be a description of all norm continuous representations.
Jan
25
revised Is a matrix element of a norm continuous representation always a trigonometric polynomial?
added 369 characters in body