24,296 reputation
266128
bio website math.purdue.edu/~eremenko
location United States
age 60
visits member for 2 years, 7 months
seen 11 hours ago
Math Professor

20h
comment Two equivalent descriptions of a physical system yielding a non-trivial mathematical formula
mathpages.com/home/kmath242/kmath242.htm
20h
comment Two equivalent descriptions of a physical system yielding a non-trivial mathematical formula
Let me add Huygens-Fresnel Principle, and Feynman formulation of quantum mechanics (which can be considered as development of this principle. Comparing two descriptions of the motion, it gives a formula for the solution of the Schrodinger equation
20h
answered Mathematical statistical qm book-recommendation
20h
comment Mass Transportation Through Wonderful Roller
Your second equation simplifies to $w(0)=w(T)$. Don't you want to add $w(0)=w(T)=0$, so there is no mass on the roller at the beginning and the end of transportation?
1d
comment Mass Transportation Through Wonderful Roller
What is $m(t)$?
Mar
23
comment An inequality based on a convex function
This is not true. Take $a=0, b=1, y=3, x=4, t=1, f(x)=x$ for $x\leq 4$ and $f(5)=10$.
Mar
23
comment If a polynomial $p(z)$ omits a value, then $p(z)-\dfrac{(1-e^{i\psi})}{n}zp^{\prime}(z)$ also omits that value
This is not true: take p(z)=z$, $\psi=\pi$, $w=1$.
Mar
22
answered Growth of a harmonic function on the disc
Mar
22
comment Growth of a harmonic function on the disc
This is for almost all $\theta$ and the question was for all $\theta$ if I understood it correctly.
Mar
22
answered Illumination of a convex body
Mar
18
comment Is the Poincaré metric continuous with respect to the domain?
Do you mean uniform convergence of $u_n$ and all derivatives to $u$ on every compact in $C\backslash K$?
Mar
18
comment Is the Poincaré metric continuous with respect to the domain?
What is the "smooth topology"?
Mar
15
comment Holomorphic Function on Disk
If $u$ is smooth in the closed disk then $v$ is smooth in the closed disk. In particular, $v$ is continuous. So $f=u+iv$ is continuous.
Mar
14
comment Holomorphic Function on Disk
Yes, if the boundary value of $u$ is smooth enough, for example, infinitely smooth. See any book on harmnic analysis, for example Zygmunt, Trig series.
Mar
13
answered Holomorphic Function on Disk
Mar
12
comment Use of an appendix in a long paper
Option 1 seems the most reasonable one. Let the referee/editor recommend other options, if they are unhappy with the length.
Mar
4
comment Boundedness of a singular integral operator on $L^p(\mathbb{R})$, $1<p<\infty$
This is essentially the Hilbert transform. Weak estimate in $L^1$ is Kolmogorov's theorem, boundedness in $L^p$ is due to Riesz. Look in Zigmund, or in Koosis or in any other book on the subject.
Feb
27
awarded  Nice Answer
Feb
21
reviewed Leave Open Causal (Volterra type) differential equation with local Lipschitz condition
Feb
21
reviewed Close Kwantitatieve Methoden