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Results tagged with cv.complex-variables
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user 16040
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
2
votes
1
answer
386
views
Entire function with special conditions [closed]
Hi all, here's my question which I have no idea how to approach.
Fix a complex number q such that |q| < 1. Describe all entire functions f such that f(z)/f(qz) is a linear function of z.
- 549
3
votes
2
answers
1k
views
Positive Fourier coefficients
Hi all,
Is there any general way to construct a smooth 2pi periodic function which vanishes on an interval and has positive Fourier coefficients?
And if that was too specific I can make this more gen …
- 549
1
vote
Accepted
Plancharel-Pólya inequality for functions of exponential type
Yes, this is true. This is Theorem 11 on chapter 2 (page 82) in R.Young's book (An introduction to nonharmonic Fourier analysis). The proof is based on an application of the Phragmén–Lindelöf principl …
- 549
1
vote
Accepted
Sampling set: relatively dense and uniformly discrete
When asking this question, in principle one should make a distinction between two cases:
When $n=1$, the space $PW_{S}$ is a space of entire functions of exponential type, with all of their unique pr …
- 549