All Questions
13,944 questions
1
vote
1
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663
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What are conditions to make f(x) defined by f(x)=f(x-1)*x + 1/e unique(for instance convex)?
[Background:]
Looking at the powerseries for the gamma-function
$ \Gamma(1+x) = 1 + a_1 x + a_2 x^2 - a_3 * x^3 + ... $
then we can arrive at a decomposition
$ \Gamma(1+x) = r(x) + g(x) $
...
- 5,342
1
vote
1
answer
190
views
cardinality of discontinuity curves of BV function
If the function $f:R\to R$ is of BV class then it has at most countably many discontinuity points (since it can be represented as a sum of two monotonic function).
I am interested to know whether the ...
- 13
2
votes
0
answers
88
views
System of 2 linear q-difference equations with singular matrix
I would like to solve the following algebraic linear system of q-difference functional equations:
\begin{cases}
a_{11}\left(x\right)f\left(x\right)+a_{12}\left(x\right)g\left(x\right)=f\left(qx\right)...
- 133
2
votes
1
answer
230
views
Completing The Space Sections in a Vectorbundle
Hi there.
Assume $(M,g)$ is a Riemanian manifold and $E\to M$ is a
vector bundle with a bundle metric $\langle\cdot,\cdot\rangle$. We then have the pre-Hilbert space $H_0:=\Gamma_c^\infty(E)$ of ...
- 23
4
votes
1
answer
474
views
Are these operators defined on 2D surfaces self-adjoint?
My research group finds/proposes a fundamental operator in quantum mechanics, the Cartesian momentum as I called (I think for mathematician the ref. 2007 is sufficient). However, I do not know whether ...
- 199
0
votes
0
answers
183
views
Continuity of the Shadow of a Nondecreasing Function
So I'm working a lot with monotone nondecreasing functions $f : [0,1] \rightarrow [0,1]$, and I'm defining a certain discrete dynamics on them. Here nondecreasing means $x < y \Rightarrow f(x) \leq ...
- 485
0
votes
1
answer
177
views
Laurent series with analytic coefficients
Let $A=H(D(0,1))$ the ring of holomorphic functions on the open unity disc.
I consider the function $f$:
$$f (t)=\sum f_{i}t^{i} \in A[[t]]$$
I suppose that the $t$-adic valuation of it is less or ...
- 3,472
2
votes
0
answers
520
views
Eigenvector of infinite matrix
I consider the system of reaction-diffusion PDEs in a ball
with Robin boundary condition.
It is a Steklov eigenvalue problem
(see G Auchmuty (2004) "Steklov eigenproblems and the representation
of ...
- 31
3
votes
0
answers
227
views
Mesh for 3d dungeons game. [closed]
Hallo, I look for some F: R^2->R height function which would generate the Speleothem ceiling http://en.wikipedia.org/wiki/Speleothem for 3d game taking place in dungeons/caves.
The function might be ...
- 139
0
votes
0
answers
227
views
Hermite function expansion
Let $f$ be a continuous function on $\mathbb{R}$ with compact support and unique maximum. Form the functions
$$
F_{n,k}(x)=f^n\left(x-\frac{k}{2^n}\right), k \in Z, n>0
$$
I am wondering if one ...
- 71
1
vote
1
answer
433
views
Intersection of ideals in C*-algebra or even rings in general
Dear all,
here is a question that has been bothering me. It goes without saying that I would appreciate any help in answering it.
Let {I_k} be a countable sequence of two sided closed ideals in a C*-...
0
votes
0
answers
74
views
Weak convergence of 4-th degrees
Good day!
We have an equation $y'+Ay=Bu$ where $y=\{\theta,\varphi\}$, $A, B$ are nonlinear operators.
$u \in L^\infty(\Gamma)$, $\theta, \varphi \in W = \{y \in L^2(0,T;V) : y'\in L^2(0,T;V')\}$, $...
- 243
4
votes
1
answer
230
views
A convergence problem about integral operator in the space of representations
This would be a basic problem in representation theory.
Let $G$ be a unimodular real Lie group, $(\pi,V)$ a smooth representation of $G$ in a Frechet space $V$. Let $f$ be a smooth function on $G$. ...
- 2,709
2
votes
1
answer
205
views
Do unitary bijections act invariantly on irreducible representations?
Let $\mathcal{A}$ be a $C^*$ algebra. Let $(\pi, \mathcal{H})$ be a faithful, irreducible, unitary, Hilbert space representation of $\mathcal{A}$; i.e., $\pi:\mathcal{A}\rightarrow\mathcal{B}(\mathcal{...
- 657
0
votes
2
answers
225
views
Codimension of $J(\omega_1)$ in its bidual
I am reading the paper
G. A. Edgar, A long James space, in: Measure Theory, Oberwolfach 1979, Lectures Notes in Math. 794, Springer-Verlag (1980) pp. 31-37.
and I am pretty confused by the remarks ...
- 3
1
vote
0
answers
318
views
Fourier series/transform of an amplitude-limited sinusoid
I am trying to estimate the amplitude of an original unlimited sine wave from a measurement of the power spectral density (PSD) of an amplitude-limited version. I expect that I may be able to do so ...
- 11
5
votes
0
answers
583
views
Cohomology of Real algebraic Varieities
I understand Serre's GAGA theorem as saying that equations over algebraically closed fields can be studied equally from the algebraic and analytic points of view, at least with respect to cohomology.
...
user2529
2
votes
1
answer
303
views
Proper sobolev spaces invariant under no-linearities
Let $f:H^s\to H^s$ at least continuous and not necesarily linear. Is there some kind of criterion or condition over $f$ that lets to ensure that $f({H^{s+k}})\subseteq H^{s+k}$?
- 151
4
votes
0
answers
273
views
Real Analytic Function and nth Prime
It is trivial that there are no polynomial function $P$ with integer coefficients that has the property $P(n)=p_n$ where $p_n$ is the $n$th prime.While it is true that can always construct a smooth ...
- 153
7
votes
0
answers
266
views
Problem with Shelah and Stern's paper on the Hanf number of the theory of Banach spaces
I have been trying to understand "The Hanf number of the first order theory of Banach spaces" by Shelah and Stern (Trans. AMS 244 (1978) 147-241). They construct a normed space $M$ from a Hilbert ...
- 879
7
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1
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570
views
Categorical duals in Banach spaces
Near the bottom of the nlab page for Banach space I see "To be described: duals (p+q=pq)".
Are $(\mathbb{R}^n)_p$ and $(\mathbb{R}^n)_q$ dual objects in the closed symmetric monoidal category of ...
- 25.2k
0
votes
1
answer
340
views
Reference for spectral theory of group of linear operators
It is not hard to find the spectral theory of a single unitary operator $U$. This is the spectral theory for a $\mathbb{Z}$-action because we consider $U^n$ for $n\in\mathbb{Z}$. This is clear with ...
- 163
2
votes
1
answer
182
views
represented as a series of periodic function
Is there any necessary and sufficient condition for function $f$ such that:
$f(x)=\sum_{k=1}^{\infty} f_k(x)$ for all $x \in \mathbb{R}$,where $(f_n )_{n=1}^{\infty}$ is a sequence of periodic ...
- 407
2
votes
0
answers
104
views
Fourier multiplier with a singularity on a convex curve
Let $h$ be a strictly convex function such that $h(0) = h'(0)=0$. Let $\Phi: \mathbb{R}^2 \to \mathbb{R}$ be a $C^{\infty}$-function with compact support (say, $\Phi$ is supported on $[-1,1]\times[-1,...
2
votes
0
answers
122
views
A parametrix for the $\bar\partial$ operator adapted to a holomorphic foliation
Let $X$ be a compact complex manifold with (regular) holomorphic foliation given by a holomorphic subbundle $\mathcal F$ of the tangent bundle. The foliation induces a filtration on differential forms....
- 51
1
vote
0
answers
92
views
Scattering solutions for $L_2$ potentials
Consider the equation
$$
Lu = -\Delta u+v(x)u = Eu, \tag{1}
$$
where $x = (x_1,x_2) \in \mathbb R^2$, $v \in L_2(\mathbb R^2)$, $E>0$. Is it known that for almost any $E>0$ and for any fixed $...
- 1,329
0
votes
0
answers
186
views
Properties of Eigenfunctions of a Kernel
I'm a newbie and may be this question is bit simple for you but pardon me if it's too simple and provide me some references.
I've and Kernel function $K(x,y)$
$f(x)=(Kg)(x)=\int_{\Omega}K(x,y)g(y)dy$...
- 17
2
votes
0
answers
202
views
Frames and reproducing kernels
Hello MathOverFlow
I have some questions about frames and reproducing kernels and here they are:
For a Hilbert space $H$ spanned by a frame $\lbrace f_n \rbrace$ there exists a reproducing kernel $K(...
- 21
1
vote
0
answers
91
views
Bound for $\Vert g\Vert_r$ when $ \Vert g-f\Vert_2<\varepsilon$
Let $f\in L^2(\mathbb{R}^n)$, $\varepsilon>0$ and $r\in[1,2)$. Define
$$ L_{r,\epsilon}:=\inf{\{\Vert g\Vert_r}:g\in L^1(\mathbb{R}^n)\cap L^2(\mathbb{R}^n),\, \Vert g-f\Vert_2<\varepsilon\}$$
...
- 21
1
vote
0
answers
615
views
Is there a Real valued function with image of every open interval the whole real line [duplicate]
Possible Duplicate:
Function with range equal to whole reals on every open set
Hello,
My problem is the following
"Is there a Real valued function with image of every open interval the whole ...
- 201
0
votes
0
answers
388
views
Global index of convexity/concavity of a function
We are looking for a global index of the convexity/concavity of a function.
For concreteness, how can I formalize the intuitive notion that a function $f$ is more convex than $g$ where $f,g:[0,1]\...
- 111
3
votes
0
answers
145
views
Growth of inner functions on the disk
Recall that an inner function on the disk $D$ is a bounded analytic function on $D$ having radial limits of modulus one almost everywhere.
There has been many works on the growth of the inner ...
- 769
1
vote
0
answers
122
views
Checking initial condition of PDE is satisfied in Galerkin method
I asked this question here: https://math.stackexchange.com/questions/416885/checking-initial-condition-of-pde-is-satisfied-in-galerkin-method
But I did not receive the solution so I post it here.
...
- 21
1
vote
0
answers
74
views
Closed for the motion of an interacting particle system
I am dealing with interacting particle systems approximately in the sense of http://www.math.vu.nl/~rmeester/onderwijs/Interacting_Particle_Systems/liggett.pdf p. 5 except I am reading a book by the ...
- 277
0
votes
0
answers
193
views
Boundedness of Riemann-like sums on unbounded interval
Hi
I am trying to find suitable conditions (integrability, growth...) on a function $f:\mathbb{R}\to \mathbb{R}$ such that:
\begin{equation}
\sum_{k\in\mathbb{Z}}f(kh)h= \mathcal{O}(1),\qquad h\to 0^+...
-3
votes
1
answer
590
views
A problem regarding definition of p-norm [closed]
Let ${\bf x}=(x_1,...,x_n)$, the p-norm of x is $(|x_1|^p+...+|x_n|^p)^{1/p}$. If one of the components of x is 0, there will be exponential of the form $0^p$. If p is an irrational, $x^p$ is only ...
- 764
5
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0
answers
616
views
Lebesgue measure on Frechet space?
It is well known that there are no Lebesgue measures on infinite-dimensional Banach spaces (see e.g. http://en.wikipedia.org/wiki/There_is_no_infinite-dimensional_Lebesgue_measure). However, I couldn'...
- 1,368
0
votes
1
answer
156
views
Does homeomorphism preserves the family of cones?
Let me state my problem. Suppose we have a ball $B$ in standard $\mathbb{R}^3$, that is a $\varepsilon$-neighbourhood of $0$ point. Suppose we have a family of cones $X_C = \lbrace C > 0 \vert x^2 +...
- 165
1
vote
0
answers
83
views
Topologies on spaces of linear sections
Let $X$ and $Y$ be topological linear spaces which are complete & Hausdorff, and admit dual spaces which separate points. Suppose the topologies are non-separable and non-metrizable.
Let $f : X \...
- 8,512
0
votes
0
answers
113
views
Reference Search for a Functional Minimization Problem
Let $u(x) \ge 0$ be a non-negative, piecewise-differentiable function on the real line. Moreover, let $u(x)$ be integrable with fixed positive mass, that is
$$M \equiv\int_{x=-\infty}^\infty u(x) ~ ...
- 151
4
votes
0
answers
158
views
Does this construction yield an injective hull ?
Let $K$ be an object of $\mathbf{CHaus}$, the category of compact Hausdorff spaces, and $K \xrightarrow{\ \ \sigma \ \ } K$ be an involutory morphism without fixed points. Define $C^{\sigma}(K)$ as ...
- 7,249
3
votes
1
answer
64
views
Complete classification of complexity classes / infinite approaching sequences
http://en.wikipedia.org/wiki/Time_complexity#Table_of_common_time_complexities
For complexity as seen in the above link, complexity classes can be log, polynomial, exp, or composition of any of these ...
- 31
1
vote
0
answers
477
views
A norm ratio inequality
Let $y,z\in(0,1)^n$ satisfy $||y||_1 = ||z||_1=1$.
Then
$$
\frac{||z||_3}{||z||_2} \le
K_n
||z/y||_\infty
\frac{||y||_3}{||y||_2}
$$
where $z/y\in\mathbb R^n$ is the coordinate-wise quotient of $z$ ...
- 6,541
0
votes
0
answers
100
views
Two distribution spaces ${\mathcal S}'/{\mathcal P}$ and ${\mathcal S}_\infty'$
Let ${\mathcal S}'$ be the set of all distributions.
Denote by ${\mathcal P}$ the set of all polynomials,
which is embedded into ${\mathcal S}'$ as a closed subspace.
Equip ${\mathcal S'}/{\mathcal P}$...
3
votes
1
answer
362
views
Cartesian product of test function spaces
Mini introduction
Suppose $U \subset \mathbb R^n, V \subset \mathbb R^m$ are two open sets. If we take http://en.wikipedia.org/wiki/Distributions_space#Test_function_space">test functions $f_i \in \...
6
votes
1
answer
369
views
Denominators in the solution to Hilbert's XVII
Hilbert's seventeenth problem asks to prove that every positive semidefinite form can be written as the sum of squares of rational functions. Currently we don't seem to have a good understanding of ...
- 85.6k
1
vote
1
answer
312
views
Invertibility of frame/sampling operator on Bargmann-Fock spaces
Let $F_\alpha ^p (\mathbb{C}^n)$ for $1 < p < \infty$ and $\alpha > 0$ be the Bargmann-Fock space defined as the Banach space of entire functions $f$ such that $f(\cdot) e^{- \frac{\alpha}{2} ...
3
votes
0
answers
163
views
Isometric automorphism of $c_0$ different than coordinate permutation
Does there exist an isometric automorphism of $c_0$ which is not a permutation of coordinates?
- 311
2
votes
0
answers
86
views
Terminology and reference question
I am working on a problem involving bilinear forms over complex Hilbert spaces, and in my case it is not natural to make the forms sesquilinear, i.e., $a(u,v)$ is linear in both complex arguments. ...
- 143
0
votes
1
answer
138
views
question about the closed form of a function
Hi everyone! I have a question about how to find the closed form of a function defined by
$$\phi(\theta)=\inf_{x\geq 2}f(x;\theta)\equiv\inf_{x\geq 2}\frac{(x+2)^2}{\frac{1}{\theta}\left(\frac{x-1}{2}...
- 69