Philipp G. Sinicyn

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bio website location Moscow, Russia age 21 member for 1 year, 6 months seen Jun 14 '12 at 17:02 profile views 49

13 Questions

 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 $\sum\limits_{s=0}^{\infty} {p-s \choose m}{q+s \choose q} = {p+q+1 \choose p-m}$

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 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

5 Accounts

 Mathematics 331 rep 110 Stack Overflow 127 rep 5 Server Fault 106 rep 1 Cross Validated 101 rep Physics 101 rep

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