martini
Reputation
51,159
97/100 score
 2h comment Operator norm of positive operator. And $A$ is positive, hence self-adjoint. 9h answered Two questions on ${\cal M}_{mn}$ of collection of matrix of $n\times m$ of maximal rank. 11h answered Prove that $x^Ty$ is diagonalisable where $x,y$ are row vectors. 2d revised Proving the result of finding the number of ways in which $N$ can be resolved as a product of two factors replaced image by TeX 2d answered find discrete numeric function of the generating function $(1+z)^n+(1-z)^n$ 2d answered properties of a separable metrizable locally convex space 2d answered Reference request: Kuratowski limit of sets 2d answered Show that the integral of absolute value of $f$ exists if $f$ is integrable. 2d answered Why are $\lambda$-systems defined with the stronger condition $A\subset B\implies B\setminus A\in\Lambda$ 2d comment Bounded linear functional $\phi \in Lip_0(X)^*$ belongs to the predual of $Lip_0(X)$ iff it is continuous with respect to the weak$^*$ topology No. $j_Y[Y]$ means the image of $Y$ in $Y^{**}$ under the canonical embedding $j_Y \colon Y \hookrightarrow Y^{**}$ 2d answered Bounded linear functional $\phi \in Lip_0(X)^*$ belongs to the predual of $Lip_0(X)$ iff it is continuous with respect to the weak$^*$ topology Nov 20 answered Express $log(E[exp(xX_t\epsilon_t) | F_t ])$ in function of $X_t$ and $x$. Nov 20 answered Verify the polynomial of degree $≤ 4$ is exact: $\int_0^1f(x)dx ≈ {1\over90}[7f(0) + 32f({1\over 4}) + 12f({1\over 2}) + 32f({3\over 4}) + 7f(1)]$. Nov 20 reviewed Leave Open Proof of a Vector Identity Using Index Notation Nov 20 reviewed Looks OK Linear Dependency and Coplanarity Nov 20 comment how do I show that generalized projection singlton? How is $\Pi_C$ defined exactly? What does it mean that $\Pi_C$ is a singleton? Nov 20 answered Finding the perpendicular vector to a vector (in a plane) Nov 20 comment Convolution of shifted dirac delta's @Salihcyilmaz So, I'd tried to write something in (hopefully) more easy notation. The idea behind $\delta$ (and other "functions", the mathematical name of these "generalized functions" is distributions), is that they only "make sense under an integral", it is they are defined by the way they act on other functions. $\delta$ is given by the property $$\int_{\mathbf R} \delta(t)\phi(t) = \phi(0)$$ for smooth $\phi$ (the integral is abuse of notation, as $\delta$ is not really a function, but it is nice to read and use). Nov 20 revised Convolution of shifted dirac delta's added 1074 characters in body Nov 20 comment Convolution of shifted dirac delta's So our background is quite different. As $\delta$ is a distribution, how do you define $\delta$ without talking about distributions?