Philipp G. Sinicyn

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331 reputation

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	location	Moscow, Russia
	age	21
visits	member for	1 year, 6 months
	seen	Jun 14 '12 at 17:02
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13 Questions

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10	Prove the identity $ \sum\limits_{s=0}^{\infty}{p+s \choose s}{2p+m \choose 2p+2s} = 2^{m-1} \frac{2p+m}{m}{m+p-1 \choose p}$
7	Solve $f(x) = \lambda \int\limits_{0}^1(\max(x,t)+xt)f(t)dt$
6	Spectrum of $\int\limits_0^x f(t) dt$ operator
6	Prove that $\sigma(AB) \backslash \{0\} = \sigma(BA)\backslash \{0\} $
6	Prove the identity $\sum\limits_{s=0}^{\infty} {p-s \choose m}{q+s \choose q} = {p+q+1 \choose p-m} $

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331 Reputation

+5	Solve inhomogeneous wave equation
+5	Prove that $Af(x) = \frac 1x \int\limits_0^x f(t) dt$ isn't compact in $L_2[0,1]$
+10	Spectrum of $\int\limits_0^x f(t) dt$ operator
+5	Prove that $\sigma(AB) \backslash \{0\} = \sigma(BA)\backslash \{0\} $

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0 Answers

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16 Tags

0 functional-analysis × 7	0 pde × 2
0 homework × 4	0 spectral-theory × 2
0 integral-equations × 2	0 binomial-coefficients × 2
0 multivariable-calculus × 2	0 combinatorics × 2
0 operator-theory × 2	0 distribution-theory

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$Mathematics Stack Exchange$	Mathematics	331 rep	110
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