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 12h comment how to define that a nonlinear operator is bounded and continuous A bounded linear operator is the same as a continuous linear operator. There is the obvious way to define continuous linear operators, if that's the generalization you're looking for. 13h comment Finding adjoint of an operator from $\mathbb{C}^n$ to $H$ @lesguimauves As user251257 said. The notation may be confusing you; I should probably have specified what space each inner product takes place in. 1d comment Proving inner measure equal to outer measure if a set is measurable Problem 19 in what textbook? Also, what is your definition of measurable? There are many equivalent definitions, including the one that makes the problem trivial, so you want to establish all definitions clearly for this problem. 1d answered Finding adjoint of an operator from $\mathbb{C}^n$ to $H$ Jul2 revised Harmonic Mean Solution removed [harmonic-functions] Jun26 comment Does there exist a continuous function from [0,1] to R that has uncountably many local maxima? @Vim It does, if you're looking at the function defined as on the Wikipedia article en.wikipedia.org/wiki/Weierstrass_function. The maximum must be at $0$ (where cosine is $1$), and there it takes the value of the geometric series with ratio $a$. However, since we care only about local maxima for this question, what is more relevant is that the Weierstraß function is continuous on every compact interval. Jun26 comment Is Fourier series used always for periodic signals and Fourier transform for aperiodic signals only? @sagar See my edit. Jun26 revised Is Fourier series used always for periodic signals and Fourier transform for aperiodic signals only? response to comment May28 answered Is Fourier series used always for periodic signals and Fourier transform for aperiodic signals only? May23 awarded real-analysis May17 comment Proof of Cauchy Schwartz inquality from Terry Tao's notes doubt The map is only $v\mapsto ve^{i\theta}$. If you apply this rotation to both $u$ and $v$, then you preserve $\langle u,v\rangle$, which is not what you want. Professor Tao's point is that in the inequality $|\text{Re}\langle u,v\rangle| \leq \frac{1}{2}(\|u\|^2 + \|v\|^2)$, there is an imbalance of rotation symmetry, and consequently there is a little wiggle room on the non-rotation-invariant LHS. Therefore the idea is to find a rotation that does not preserve the LHS, and $v\mapsto ve^{i\theta}$ is enough. May15 answered Proof of Cauchy Schwartz inquality from Terry Tao's notes doubt May1 revised Inverting a map from a finite 3D grid to 1D removed [computational-complexity] tag May1 reviewed Approve Physical significance and graphical point of view of second derivative of a function $f''(x)$ . May1 reviewed Approve Calculus limits with sin and cos May1 comment function constant on arc is constant on boundary @MichaelHardy I don't see any of your comments on that question...is there a reason you're asking me in particular? This seems rather random. Apr30 reviewed Close Proving that $\sum \limits_{d^2|n}\ \mu (d)=\mu^2(n)$, where $\mu$ is the Möbius function. Apr30 reviewed Close Error function etymology: Why the name? Apr30 reviewed Leave Open The difference between the ring version and module version of Chinese Remainder Thereom. Apr30 reviewed Leave Open Properties of Infinite Limits