Bazin
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Registered User
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6h |
comment |
Is a Cauchy principal value invariant under a “change of variables”? You are right, I have changed my answer and added some explanations on Calderon-Zygmund operators. |
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6h |
revised |
Is a Cauchy principal value invariant under a “change of variables”? added 1185 characters in body |
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7h |
revised |
Is a Cauchy principal value invariant under a “change of variables”? added 169 characters in body |
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18h |
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Is a Cauchy principal value invariant under a “change of variables”? With the bi-Lipschitz continuity hypothesis, for every $\delta>0$, you get $\epsilon,\sigma >0$ such that $$ \\{\vert G(v)-G(w)\vert\le \sigma\\}\subset\\{\vert v-w\vert\le \delta\\}\subset\\{\vert G(v)-G(w)\vert\le \epsilon\\} $$ implying that last step. |
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1d |
answered | Is a Cauchy principal value invariant under a “change of variables”? |
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May 13 |
answered | about smoothing pseudodifferential operators |
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May 8 |
answered | Is there an equivalent of Heisenberg’s uncertainty principle in the decision sciences ? |
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May 8 |
accepted | Infinite Real Symmetric Toeplitz Matrix Reference |
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Apr 27 |
accepted | Is there existence and uniqueness theory of this system of ODE? |
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Apr 25 |
answered | Is there existence and uniqueness theory of this system of ODE? |
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Apr 24 |
answered | Replacing large-dimensional ODE systems with one PDE |
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Apr 22 |
answered | Can a nowhere continuous function be integrable ? |
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Apr 18 |
comment |
Applications of pseudodifferential operators to PDE Bazin (mathoverflow.net/users/21907), Motivation for and history of pseudo-differential operators, mathoverflow.net/questions/97604 (version: 2012-05-23) |
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Apr 16 |
answered | Nonharmonic solutions of Laplace’s equation |
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Apr 15 |
answered | Does the derivative of log have a Dirac delta term? |
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Apr 14 |
answered | Increasing regularity for $L^2$ function |
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Apr 13 |
answered | Polynomial growth of Fourier transforms |
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Apr 13 |
answered | Oscillatory Integral |
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Apr 10 |
answered | Global Implicit Function Theorem |
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Apr 9 |
awarded | ● Nice Answer |
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Mar 25 |
answered | Smoothness of $f(\sqrt x)$ |
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Mar 22 |
accepted | The Periodic Schrödinger Group |
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Mar 22 |
answered | The Periodic Schrödinger Group |
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Mar 20 |
accepted | Every function in W^{1,1}(0,1) is continuous on (0,1) |
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Mar 13 |
accepted | Embedding of weighted Sobolev spaces |
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Mar 13 |
comment |
Embedding of weighted Sobolev spaces Yes of course, because of the $(1+\vert x\vert^2)^s$, locally in $x$ comparable to 1. |
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Mar 13 |
answered | Embedding of weighted Sobolev spaces |
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Mar 12 |
answered | problem related to airy function |
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Mar 10 |
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Eigenfunctions of elliptic operator form an orthonormal basis for L_2? I meant compact manifold without boundary. |
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Mar 9 |
answered | Eigenfunctions of elliptic operator form an orthonormal basis for L_2? |
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Mar 9 |
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analysis of the regularity using Hormander condition @Kamil I agree with you on this shrinking business. However, my claim is that the method suggested by my answer is providing an explicit integral solution for your problem. With that explicit solution, you should be able to decide the smoothness properties. |
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Mar 9 |
answered | Every function in W^{1,1}(0,1) is continuous on (0,1) |
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Mar 7 |
accepted | Analogue of the integral Fourier operator with angle in some cone |
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Mar 6 |
awarded | ● Yearling |
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Feb 28 |
accepted | About the boundedness of a multiplication operator. |
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Feb 26 |
answered | Solving Stokes Equations using 3D Fourier transforms |
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Feb 25 |
answered | About the boundedness of a multiplication operator. |
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Feb 24 |
answered | Nth root of a matrix as an analytic function? |
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Feb 24 |
answered | Class of functions that the Fourier inversion holds |
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Feb 23 |
answered | Pullback measures |
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Feb 22 |
revised |
First Order PDE Solution Method Issues added 1099 characters in body; added 1 characters in body |
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Feb 22 |
comment |
First Order PDE Solution Method Issues @ sponsoredwalk I added a couple of comments on the quasilinear case. |
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Feb 21 |
answered | First Order PDE Solution Method Issues |
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Feb 20 |
accepted | An interpolation inequality. |
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Feb 19 |
comment |
An interpolation inequality. The only problem is when $\epsilon$ is small, and you do have a singularity at $\epsilon=0$. Now for $x>1,0<\epsilon<1/4$, $$ \frac{x-1}{2}\ln(1-\epsilon)\le\frac{x(-\epsilon/2)}{2} $$ so you can take $a=1/4$. The bounded values of $x$ are unimportant. |
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Feb 19 |
revised |
An interpolation inequality. deleted 1 characters in body |
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Feb 18 |
answered | An interpolation inequality. |
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Feb 16 |
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analysis of the regularity using Hormander condition I have made an explicit computation and you can find as well an explicit solution with my formula above by plugging the values of $v$ in terms of your $u$. The regularity business, say for the function $v$ follows from the explicit integral expression: you get easily that the $L^2$ norm of $\mathcal K v$ controls the $H^1$ norm in the $x$ variable of $v$. The expression of $w$ shows that you control 2/3 of derivatives for the $z$ variable: if you want an isotropic control then you cannot do better than $2/3$. To see that is not completely obvious: just compute exactly the integral in the phase |
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Feb 16 |
answered | Analogue of the integral Fourier operator with angle in some cone |
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Feb 10 |
accepted | Exponential stability in nonlinear differential equations |
