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Hiro
  • Member for 3 years, 9 months
  • Last seen more than a month ago
5 votes
2 answers
108 views

Prove that $K \ast f \in W^{1,\infty}(\mathbb R)$ if $K \in BV(\mathbb R)$

3 votes
1 answer
187 views

A special approximation of the Heaviside function

2 votes
0 answers
39 views

Kolmogorov $\epsilon$-entropy, $n$-width, and $\epsilon$-capacity and applications

1 vote
1 answer
120 views

Functions such that $ \Vert\tfrac{d^4}{dx^4}f\Vert_{L^2(0,1)} < \sqrt{2} \Vert f \Vert_{L^1(0,1)}$

1 vote
0 answers
105 views

Series and solution of $-\Delta u + \lambda u = f(x)$

1 vote
2 answers
193 views

How can I prove that $(I+\lambda G)$ is invertible, where $G$ is the Green function of an elliptic operator?

1 vote
0 answers
42 views

Uniform bound on the measure of $\Omega_\delta = \Omega \cap \delta\mathbb Z^d$ if $\Omega$ is an open bounded set with Lipschitz boundary

1 vote
1 answer
255 views

Is $(f \ast K)'' \in L^1(\mathbb R)$ for $f \in L^1 \cap L^\infty(\mathbb R)$ and $K \in BV(\mathbb R)$?

1 vote
1 answer
387 views

Computing the fractional Laplacian of power function

0 votes
0 answers
49 views

$L^p$ estimate for perturbed heat equation

0 votes
1 answer
99 views

Functions for which $|f^{(k)}|_{C^{0,\alpha}(0,1)} \le \Vert f \Vert_{L^1(0,1)}$

-1 votes
1 answer
90 views

Is it true that $\nabla_x \int_0^\infty f(t,0) dt = 0 \implies \nabla_x f(t,0) = 0 \ \forall t>0$? [closed]