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user23078
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38 votes
5 answers
5k views

Why is symplectic geometry so important in modern PDE ?

18 votes
6 answers
2k views

What's the use of Malgrange preparation theorem?

18 votes
2 answers
6k views

What's the idea behind Carleman estimates?

11 votes
1 answer
616 views

What's the role of $H^{p}(\mathbb{R}^{n})$ in modern (harmonic) analysis?

11 votes
2 answers
1k views

what's the motivation of Weyl calculus ?

8 votes
2 answers
2k views

(sharp)Garding's inequality and inequality with lower bounds

7 votes
2 answers
2k views

when a pseudo-differential operators to be compact?

6 votes
6 answers
2k views

Fractional Leibniz formula

4 votes
2 answers
526 views

What do we know about the semigroup $e^{it\sqrt{-\Delta}}$

4 votes
0 answers
931 views

Resonance of Schrödinger operator

4 votes
1 answer
273 views

Is there a good way to estimate the Fourier transform of $\frac{1}{\lambda-iP(\xi)}$

3 votes
1 answer
626 views

Is this kernel space of finite dimension ?

2 votes
1 answer
250 views

Fourier transform and spectrum of PDOs in $L^p$

2 votes
1 answer
273 views

Fourier transform of a particular function

2 votes
2 answers
518 views

Fourier transform of $e^{it|\xi|^{\alpha}}$

1 vote
1 answer
1k views

Almost analytic continuation

1 vote
1 answer
2k views

The fourier transform of homogeneous distribution and related topics

1 vote
2 answers
396 views

Does these commutator estimates bound in $L^{2}$

1 vote
1 answer
3k views

how to prove the range of a closed linear operator is closed ?

0 votes
3 answers
881 views

Higher order fractional laplacian

0 votes
1 answer
158 views

Convolution operators defined by compactly supported distribtion

0 votes
1 answer
725 views

Wave equation v.s.Schrödinger equation