dimension

Call a polynomial balanced if its average value over every circle centered at zero is zero. The of all polynomials of degree forms a vector space . Find .

So what basis this you use?

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Originally Posted by Sampras

Call a polynomial balanced if its average value over every circle centered at zero is zero. The of all polynomials of degree forms a vector space . Find .

So what basis this you use?

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I used rank nullity.

the set of polynomials with degree less or equal a certain natural ,is a subspace with dimension equal to .