T.A.E.
Reputation
18,485
Next privilege 20,000 Rep.
Access 'trusted user' tools
2 5 31
Impact
~82k people reached

 12 Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$ 11 Improper integral of $\int_0^\infty \frac{e^{-ax} - e^{-bx}}{x}\ dx$ 9 Show that $\int_0^{2\pi}\frac{R^2-r^2}{R^2 - 2Rr\cos (\varphi-\vartheta) + r^2}d\vartheta$ is independent of $R>r>0$, using only real numbers. 8 If a linear operator has an adjoint operator, it is bounded 7 Complex analysis is more “real” than real analysis

### Reputation (18,485)

 -2 showing $\inf \sigma (T) \leq \mu \leq \sup \sigma (T)$, where $\mu \in V(T)$ +10 Let $f:(a,b)\rightarrow \mathbb{R}$ be non-decreasing i.e. $f(x_1)\leq f(x_2)$ and let $c \in (a,b)$. Show that limits from both sides exist. +30 Inverse of $I +T^*T$ +15 Higher Order ODE with Differential Operators

### Questions (20)

 7 Essential Selfadjointness of Quantum Harmonic Oscillator Hamiltonian 5 Is there a cyclic vector for $-\frac{d^{2}}{dx^{2}}$ on $L^{2}[0,2\pi]$ with periodic conditions? 5 How to show $e^{-x}$ is a cyclic vector for $-\frac{d^{2}}{dx^{2}}$ in $L^{2}[0,\infty)$? 5 Simple proof that $\|p(A)\|\le \sup_{|z|\le 1}|p(z)|$ for polynomials $p$ and $\|A\| \le 1$. 5 Show that $\|e^{tA}\| \le e^{t\|\Re (A)\|}$

### Tags (211)

 589 functional-analysis × 511 136 linear-algebra × 125 223 operator-theory × 201 91 fourier-analysis × 94 212 real-analysis × 170 90 analysis × 81 150 hilbert-spaces × 117 84 complex-analysis × 65 149 spectral-theory × 113 78 calculus × 51

### Accounts (3)

 Mathematics 18,485 rep 2531 Biblical Hermeneutics 184 rep 1 MathOverflow 111 rep 3