All Questions

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Fourier Transform of compactly supported L^1 functions

Background Given a (translation bounded) positive definite measure $\gamma$ lets say on $\mathbb R^d$, it's Fourier transform as a Tempered distribution is a positive measure $\widehat{\gamma}$. I am ...
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how many graphs can be drawn if n vertices ara given [on hold]

If there are n vertices then number of undirected graphs can be defined as nc0+nc1+nc2........ncn. i.e combination of one vertex + combination of two vertices . Can anybody please help me in making ...
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Inequality involving the side lengths of a quadrilateral

If $a$, $b$, $c$ and $d$ are the four sides of a quadrilateral, the problem is to show that $ab^2(b-c)+bc^2(c-d)+cd^2(d-a)+da^2(a-b)\ge 0$. I've verified it to be true for quite a large number of ...
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About the trace class operators and their motivation

What is the motivation for trace class operators? Can any body suggest the most general and standard reference that includes Schatten p class operators as well. I have following references ...
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Spectral measure and Stone's theorem

Let $T$ be an unbounded self-adjoint operator on a Hilbert space and let $E(\lambda )$ be the associated spectral measure and $R(\lambda ) = (T-\lambda )^{-1}$ the resolvent. By Stone's theorem we ...
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Iwasawa algebra

Suppose $M$ is a finitely generated torsion $Z_p[[T]]$-module; the torsion comes from the $\mu$-invariant part and the $Z_p$-part (the $\lambda$-invariant). Now consider $M/(p)$ and $M[p]$ ...
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Smooth structures on quotient space

Suppose $G$ be a discreat group acting on $\mathbb R^n$ freely via two different actions $\rho_1$ and $\rho_2$. Suppose that $\mathbb R^n/\rho_1$ is homeomorphic to $\mathbb R^n/\rho_2$. However the ...
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Problem with understanding an equation

I have read the article Short-wavelength Spectral Properties of the Gravity Field from a Range of Regional Data Sets and I don't know how to interpret Equation (10) on page 630, because this equation ...
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Is the universal elliptic curve $\overline M_{1,2}$ a toric stack?

It is well-known that the compactification $\overline M_{1,1}$ of the moduli space of elliptic curves over $\mathbb C$ is a weighted projective line with weights $4$ and $6$. As far as I can tell, ...
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Intuition for ample line bundles [migrated]

Let $X\subset \mathbb{P}^N$ be a smooth projective variety over $\mathbb{C}$. We let $\mathcal{O}_X(n)$ denote the bundle induced by $\mathcal{O}_{\mathbb{P}^N}(n)$. For a coherent sheaf $F$ on $X$, ...
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Parameter dependent differential equation in a Lie group

It is well-known that a linear differential equation in a finite-dimensional vector space depends continuously on some external parameters (for details see below). Is there a work which extends this ...
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algebraicity of Néron-Tate canonical height for Abelian varieties over global function fields

(transcendence of canonical heights) Is the Néron-Tate canonical height for an Abelian variety $A$ over a global function field $K$, $\hat{h}: A(K) \times A^\vee(K) \to \mathbf{R}$ known to always ...
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comparison of two bundle structure for second tangent bundle [migrated]

Let M be a manifold and \pi :TM \righarrow M is the standard projection. The second tangent bundle T^2M is a vector bundle on TM in the following two natural ways: 1)Put N:=TM with a natural ...
For topological spaces $S$ and $T$, denote by $C(S)$ and $C(T)$ the corresponding algebras of continuous real-valued functions. What are the necessary conditions that we need to impose on $S$ and $T$ ...
When for every module $M$, $|E(M)| = |M|$
Is there a non-semisimple ring $R$ such that for any left $R$-module $M$, $|E(M)| = |M|$ ? (where $E(M)$ is the injective hull of $M$ and $|M|$ is the cardinality of $M$)