I had been having a hard time keeping πειράω (to try, test) and πείρω (to go through, pierce) straight. Then I realized that there is a noun πείρα, and it suddenly made sense: go through → a trial is something you go through → to try.
Flipping through a dictionary to look for verbs ending in -άω, I found three or four, and they all seemed to have matching feminine nouns that end in -α or -η.
Is it always/usually true that a verb with this ending has been formed in this way? If so, does it have any specific semantics, or is it just a generic way of changing the part of speech so it becomes a verb? Is there something similar for second and third declension nouns?
According to Schwyzer 1939 (Griechische Grammatik), vol. I p. 673 you are right: „Denominativbildungen auf -εω, -αω, -οω", Smyth 1918 (Greek Grammar), § 866 :“ -αω : derived chiefly from words with a stems …. Verbs in -αω denote to do, to be, or to have, that which is expressed by the stem“.
In this retrograde lexikon (Kretschmer-Locker Rückläufiges Wörterbuch der griechischen Sprache), one can find a lot of αω-verbs (archive.org has this book to borrow: https://archive.org/details/rcklufigeswrterb0000kret).
Thanks, Jean, that was exactly what I was looking for!
According to Smyth (for the convenience of others who come across this thread), the -εω verbs are usually formed from nouns that have an -ο stem that has an alternate -ε form, such as οἶκος and φίλος. So that was why I wasn’t seeing that from flipping through a dictionary.
Based on the Homeric glosses I’ve accumulated, https://github.com/bcrowell/ransom/tree/master/glosses , it looks like -εω is the most common, -αω is about three times less common, and -ευω about three times less common again.