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I am a professor of Mathematics at the University of Pisa, Italy.


1d
comment Supremum of positve kernel
..and you can apply the finite dimensional result to $P_\pi T P_\pi $, where $P_\pi $ is the orthogonal projector on $L^2$ wrto the sub-algebra generated by a finite measurable partition $\pi$. Taking a limit on the partitions you get the stated equality.
Jan
28
comment Riemann Siegel function and gamma function
Yes, but if a question originates a non trivial and interesting answer, it shouldn't be that bad. Anyway, I respect your sportsman-like attitude.
Jan
28
comment Riemann Siegel function and gamma function
I'm curious about this unusual phenomenon (yet expected, by the "Reversal" badge) of +15 points difference between question and answer! Some hints?
Jan
28
reviewed Close Sequence of smooth maps converging to the identity
Jan
28
reviewed Leave Open An integral with respect to the Haar measure on a unitary group
Jan
28
comment Gateaux but not Frechet differentiable functional
You can see the difference between Gateaux vs Fréchet already in $\mathbb{R}^2$. Since you asked for an example in $L^p$, it is worth recalling that there are very natural examples of nonlinear operators on $L^p$ spaces which are G but not F differentiable. If you need this for your class' needs, you may like to check "A primer on Nonlinear Analysis" by A.Ambrosetti and G.Prodi, a very nice and elementary introduction to Nonl.Anal.
Jan
28
reviewed Leave Open Approximating an arbitrary $\sigma$-algebra by simpler $\sigma$-algebras
Jan
28
reviewed Leave Open Approximation of quadratic variation
Jan
28
reviewed Leave Open Simplify the product $ I_{\nu}(\delta_1 \sqrt{x}) I_{\mu}(\delta_2 \sqrt{y-x}) $ of modified Bessel functions of the first kind
Jan
28
reviewed Leave Open Question on the local existence theory for the classical solution for the incompressible fluid dynamics equation
Jan
28
comment Sequence of smooth maps converging to the identity
You just want the Inverse Function Theorem, the very classical and elementary one (only, not all statements of it take care of the size of $\epsilon$). Local $C^1$ convergence is enough (while of course just $C^0$ is not). Check e.g. the second application listed here: en.wikipedia.org/wiki/Banach_fixed-point_theorem#Applications
Jan
28
reviewed Leave Open Lagrange Multipliers for linear functionals
Jan
28
reviewed Leave Open distances-based dispersion measuring approach
Jan
28
comment Is there a standard notation for off-diagonal transpose?
Without introducing new notations, this is $PA^TP$, with the matrix $P=[[0,1],[1,0]]$ .
Jan
27
comment Continuous-piecewise-linear versus piecewise-linear
sorry, I didn't realize it, and in the meanwhile I had some piecewise linear arcs my head.
Jan
27
answered Continuous-piecewise-linear versus piecewise-linear
Jan
26
revised Legendre transform and Lipschitz approximation
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26
revised Legendre transform and Lipschitz approximation
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Jan
26
revised Legendre transform and Lipschitz approximation
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Jan
26
revised Legendre transform and Lipschitz approximation
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