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Aug 4, 2021 at 8:50 vote accept Steve
Aug 3, 2021 at 21:25 comment added Iosif Pinelis @Steve : Yes, this is another way to come to the same conclusion.
Aug 3, 2021 at 21:13 comment added Steve Thank you so much for your pointer. From Section 4.1.3 of this paper, Gaussian process can be represented as an infinite sequence $\sum_{i\in I} z_i \cdot \lambda_i ^{1/2} \phi_i$ where $z_i \sim N(0,1)$. Indeed the RKHS norm of $f\sim \mathcal{GP}$ is infinity.
Aug 3, 2021 at 18:35 history answered Iosif Pinelis CC BY-SA 4.0