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Feb
8
asked If $T$ is an orthogonally diagonalizable linear operator in an inner product space, show that $T^*$ is also orthogonally diagonalizable.
Feb
6
asked Let $\{e_1,\ldots,e_n\}$ be an arbitrary basis in a finite dimensional inner product space. Prove $\exists \{f_1,\ldots,f_n\}: (e_i,f_j)=\delta_{ij}$
Feb
4
asked What general mobius transformation maps $|z-1|=1$ to itself and $|z+1|=1$ to $|w-3|=3$.
Feb
2
asked If $f$ is analytic in $D$ and $|f(z)|<M$ everywhere on $|z|=1$, show for all $z:|z|<1$, $|f(z)| \leq M |\frac{z-a}{\bar a z - 1}|$
Feb
1
asked Let $V$ be the space of complex polynomials on $[0,1]$. Is the differentiation operator self-adjoint?
Jan
30
asked Suppose $T$ is diagonalizable in $\mathbb{C}$. Show $e^T = \sum_{\lambda \in sp(T)} e^\lambda P_\lambda$ is the matrix exponential series.
Jan
17
asked (Ahlfors, p198) Why is it clear we can write $G(z-1)=ze^{\gamma(z)}G(z)$ when deriving the Gamma function?
Jan
16
asked Laurent expansion of $1/(1+z^n)$ for $n \in \mathbb{N}$.
Jan
13
asked Let $f(x) = (x^n-1)/(x-1)$. Why does $f(1)=n$?
Jan
1
asked Let $f(z) = \frac{z^{-2}}{\sin( \pi z )}$. What is the residue for $z \neq 0$?
Dec
20
asked What is the formula for a likelihood ratio $L$ that transforms martingale Geometric BM to Geometric BM with positive growth?
Dec
18
asked What is the statistical steady state of this poisson process?
Dec
16
asked Suppose $X_{n+1} = 2X_n - X_{n-1} + Z_n$. What is the value function and backward equation to calculate $P(X_T > 1 \mid X_0 = X_1 = 0)$.
Dec
13
asked Suppose $X_t$ is a brownian motion with $X_0 \sim u_0$. What is the probability density of $X_t$? (heat equation)
Dec
10
asked Suppose $dX_t = a(X_t) dt + b(X_t) dW_t$ and $Y_s=X_t$ where $s=t^2$. What SDE does $Y_s$ satisfy in the weak sense?
Dec
5
asked Is the determinant of $A$ is equal to the product of its eigenvalues for vector spaces over any field?
Nov
22
asked What is the conditional distribution of $X_3$ where $dX_t = adt + dW_t$?
Nov
20
asked How to solve the following PDE for A and B?
Nov
19
asked Show $f_t- a x f_x + \frac{1}{2} b \sigma^2 f_{xx}=0$ has solutions of the form $f(x,t) = C(t) e^{-D(t)x^2}$
Nov
14
asked Find the limiting joint distribution of $X_n$ and $X_{n-1}$ as $n \to \infty$