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Results tagged with ca.classical-analysis-and-odes
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user 89123
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
5
votes
1
answer
672
views
Number of zeros of a real analytic function
Let $f(x,y,t):[-1,1]^3\to \mathbb{R}$ be a real-analytic function. Assume that for any fixed $x,y$, $f(x,y;t)$ is not a constant function $[-1,1]\to \mathbb{R}$. Since the zeros of a non-constant real …
- 187
1
vote
0
answers
142
views
About the computation of the inverse Laplace transform [closed]
I have several questions about the inverse Laplace transform:
If $F(s)$ is a smooth real-valued function vanishing on a large subset of $\mathbb{R}$ (e.g. $F(s)$ is supported on a bounded interval), …
- 187
3
votes
1
answer
475
views
Is there a uniform upper bound for this oscillatory integral?
I am wondering whether the following uniform upper bound holds:
$|\int_a^{2a}\frac1t\sin(N b^2t)\exp(iNbt^2)dt|\le Cab^2,$
where $0<a<b<1$, $N>N_0(a,b)\gg1$, and $C$ is a constant independent of $N, …
- 187
3
votes
1
answer
167
views
Uniform bound for an oscillatory sum
I am wondering if there is a uniform bound $C$ (independent of $\lambda>10$):
$$\sum_{k=-\infty}^{-1}\Big|\int_{2^k}^{2^{1+k}}\frac{\sin(\lambda t^3)}{t}dt\Big|\le C.$$
Remark: (1) An easy upper boun …
- 187