Theorems · Theorem · complex analysis
continuousOn_herglotzRieszKernel_sphere
∀ {R : ℝ} {w c : ℂ}, w ∈ Metric.ball c R → ContinuousOn (herglotzRieszKernel c w) (Metric.sphere c |R|)The Herglotz–Riesz kernel herglotzRieszKernel c w is continuous on the circle sphere c |R|
whenever w ∈ ball c R.
- Defined in
- Mathlib.Analysis.Complex.Poisson
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- absstatement and proof · cited by 1,814
- ContinuousOnstatement · cited by 1,411
- Metric.ballstatement and proof · cited by 735
- Metric.spherestatement and proof · cited by 371
- continuousOn_id'proof · cited by 109
- continuousOn_constproof · cited by 96
- ContinuousOn.fun_subproof · cited by 18
- herglotzRieszKernelstatement · cited by 14
- ContinuousOn.divproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- hasDerivAt_circleAverage_herglotzRieszKernel_smulproof · cited by 1
- re_circleAverage_herglotzRieszKernel_smulproof · cited by 0