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1h
revised geometric interpretation of Lie bracket
added 10 characters in body
23h
comment How to numerically evaluate a integral whose limits are functions of x (using Gauss quadrature rule)?
I know what $\int_x^1 qdq$ means, but what would $\int_q^1 dq$ mean?
1d
comment Atiyah-Guillemin-Sternberg Theorem for current
How do you define the moment map if the form is singular? Can you give an example of a Kahler manifold where the induced symplectic form is singular?
1d
revised Random processes with smooth paths
added 92 characters in body
1d
answered Random processes with smooth paths
2d
revised Nice way to express $H^{-1}(\mathbb{S}^1)$
added 218 characters in body
2d
comment Nice way to express $H^{-1}(\mathbb{S}^1)$
I'll add details to the answer.
2d
answered Nice way to express $H^{-1}(\mathbb{S}^1)$
Apr
29
comment approximating smooth functions by non-smooth ones, in the distribution topology
Firs, the space $\mathscr{D}$ is not a normed space so you cannot speak of the norms of linear functionals. From the definition of the topology on $\mathscr{D}'$ it follows that the operator $\frac{d}{dx}$ is continuous on $\mathscr{D}'$. For more details see L. Schwartz book on distributions.
Apr
28
comment Can the topological algebra of analytic functions be endowed with a norm that defines the natural topology?
Can you define the "natural topology" on this algebra?
Apr
26
comment Set of General Linear Position with Nonzero Measure
Can you define precisely the concept of general linear position?
Apr
25
revised Zeroes of global sections killed by differential operators
deleted 2 characters in body
Apr
25
answered Zeroes of global sections killed by differential operators
Apr
25
comment $p$-adic Dirac measure as a weak limit
Set $B_{1/n}=\{x;\;\;|x|_p\leq 1/n\}$ set $v_n=\mu(B_{1/n})$, $\mu=$ Haar mesure, $\delta_n(x)=\frac{1}{v_n}I_{B_{1/n}}(x)$, where $I_A$ is the indicator function of a set $A$.
Apr
25
comment How to learn concepts of Functional Analysis which are common in PDE
The concept of weak topology/convergence is very well discussed in Chap.3 of Brezis' book. This will cover 99% of the situations you will encounter when investigating pde-s. In fact I would recommend that you first read Brezis before you read more sophisticated discussions of spaces in duality. In particularly, I have not seen anywhere discussed so efficiently the direct method in the calculus of variations (Corollary 3.23 in Brezis).
Apr
23
comment Recursively calculate the determinant
Don't worry about the meaning of $\otimes$. What I wrote is equivalent with your definition. My not-really-an-answer makes two points: 1). it suffices to assume the matrices $\Sigma_{ii}$ are diagonal; 2) even the simplest case $p_1=\cdots =p_k=1$ is nontrivial.
Apr
23
revised Recursively calculate the determinant
added 1 character in body
Apr
22
comment Why do people study representations of 3-manifold groups into $SL(n,\mathbb{C})$?
What is the nice complete set of invariants supplied by the geometrization conjecture? What about the classification of knots and links? They are determined by their complements which are $3$-manifolds with boundary. Deciding whether two knots are isotopic is still a very difficult problem.
Apr
22
comment Constancy theorem for integral currents
In the above statement $A$ hast to be connected! Without this assumption the result is not true.
Apr
22
answered Recursively calculate the determinant