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11422
bio website math.vt.edu/people/renardym
location Blacksburg, VA
age 59
visits member for 3 years, 5 months
seen 10 hours ago

16h
reviewed Approve suggested edit on Petersson product of newforms to different level
19h
comment Does there exist a base $\{e_j\}_{j\geq 1}$ of $H(\Omega)$ such that $\{e_j\}_{j\geq 1}$ is linearly independent in $L^2(\omega)^d$?
You can use the Stokes operator with slip conditions instead.
2d
comment Does there exist a base $\{e_j\}_{j\geq 1}$ of $H(\Omega)$ such that $\{e_j\}_{j\geq 1}$ is linearly independent in $L^2(\omega)^d$?
Take the eigenfunctions of the Stokes operator. They are analytic in $\Omega$, so if any linear combination vanishes in $\omega$, then it also vanishes in $\Omega$.
Apr
18
reviewed Approve suggested edit on Projective modules over noncommutative tori?
Apr
7
comment Is any derivative of $f_1^x f_0^{1-x}$ w.r.t. $x$ integrable?
For any x in the strip, $f_1^xf_0^{1-x}$ is integrable. Now express the derivatives as contour integrals of the function using Cauchy's formula.
Apr
7
comment on high order Laplacian
You may start with a literature search under the keyword "fractional diffusion."
Apr
7
answered Is any derivative of $f_1^x f_0^{1-x}$ w.r.t. $x$ integrable?
Mar
29
answered Find sufficient and necessary conditions on $f$ in which the level curve $f(x,y)=0$ implies only one case $x=a$ for all real $y$
Mar
29
awarded  ca.analysis-and-odes
Mar
28
answered How to integrate an exponential function of an exponential function?
Mar
27
comment Teaching profession:Differential Equations and Mean Value Theorems
You do not mention where you are teaching this course. If you are talking about an average university in the US, I wish you luck. You will need it.
Mar
26
reviewed Reject suggested edit on Which Lie groups have adjoint representations that are bounded away from zero?
Mar
24
comment Implementing boundary conditions to an ODE (involving elliptic integrals)
You can have a solution with a singularity at x=0 only if a=k or a=-k.
Mar
24
comment Periodic solution of first order ODE
What do numerical calculations suggest? If you have not done those, I suggest you put this question on hold until you have.
Mar
19
comment how to solve this system of nonlinear differential equations
The separate discussion of this special case is, as we usually say, left as an exercise to the reader.
Mar
19
answered how to solve this system of nonlinear differential equations
Mar
12
comment Question on center-stable manifold
I think $\gamma^+(x)$ is the forward orbit through $x$ and $\omega(x)$ is the $\omega$-limit set of that orbit.
Mar
6
comment Simultaneous Orthogonal basis for $L^2(\mathbb{R}^n)$ and $H^1(\mathbb{R}^n)$
However, if we are content with orthogonality with respect to an equivalent inner product in one of the spaces, then it can be done. For a lot of purposes, this might be enough.
Feb
26
answered Fractional laplacian of radially symmetric functions
Feb
23
comment Reference for invariance of essential spectrum under relatively compact perturbations
This site should not become a shortcut to substitute for literature searches. Voting to close.