Leon P Smith on Nostr: npub1zdp33…2vqv8 I'm not really qualified to speak in any depth on Real Analysis, ...
npub1zdp33shl69xr0uq3x8n5gsjykq9upycwh6nqm02c3f6x0frrn0dq42vqv8 (npub1zdp…vqv8) I'm not really qualified to speak in any depth on Real Analysis, but I'm all but certain the answer is "yes, there are such functions".
The analytic functions we all know and love and that the first two or more years of calculus spends all of it's time on, are extremely unusual.
If you can resolve the function in sufficiently high detail in the neighborhood of literally any point in the domain, you can derive the behavior of the function across its entire domain. Clearly many/most "real world" functions do not have this property, which depends on having relatively "nice" derivatives all the way down.
You might be able to find something that is what you are looking for, or close to it, in say Counterexamples in Analysis by Gelbaum and Olmstead. This seems like it should be a basic enough question for anybody who has a respectable understanding of Real Analysis, but that's not me.
The analytic functions we all know and love and that the first two or more years of calculus spends all of it's time on, are extremely unusual.
If you can resolve the function in sufficiently high detail in the neighborhood of literally any point in the domain, you can derive the behavior of the function across its entire domain. Clearly many/most "real world" functions do not have this property, which depends on having relatively "nice" derivatives all the way down.
You might be able to find something that is what you are looking for, or close to it, in say Counterexamples in Analysis by Gelbaum and Olmstead. This seems like it should be a basic enough question for anybody who has a respectable understanding of Real Analysis, but that's not me.