Does an inequality of infinite sums imply another?
Suppose $A, B$ are (infinite) sets of Euclidean vectors with $\sum_{\substack{y \in A}}||y||^{-2} \leq \sum_{\substack{z \in B}}||z||^{-2}$ Can we conclude $\sum_{\substack{y \in A}}e^{-\tau||y||^2} \leq \sum_{\substack{z \in B}}e^{-\tau||z||^2}$, for all positive real numbers $\tau$?
Intuitively this seems true, but there may be something I'm not taking into account. I can raise the bounty if the question proves difficult.

43
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1.6K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 237 views
- $20.00
Related Questions
- Extremal values/asymptotes
- Calculus word problem
- Please help me with this math problem I am struggling!
- Find $\lim _{x \rightarrow 0} x^{x}$
- Integration
- Plot real and imaginary part, modulus, phase and imaginary plane for a CFT transform given by equation on f from -4Hz to 4Hz
- Prove that $tan x +cot x=sec x csc x$
- Help with Business Calculus problem.