Who are the known authors of the psalms?

It has long been known that while King David of the Israelites wrote 74 of the Psalms (www.ifcj.org/site "Psalms of David"), 47 have no known author and 29 are attributed to other authors (there is some difference between sources in attributing 73 or 74 psalms to David):

David, Psalms 3-41, 51-66, 68-70, 86, 101, 103, 108-110, 122, 124,131, 138-145 (74)
Others:
Asaph / Sons of Asaph, Psalm 50 and 73-83 (12)
Sons of Korah, Psalms 42-49, 84-85, 87-88 (12)
Solomon, Psalms 72 and 127 (2)
Moses, Psalm 90 (1) Heman, Psalm 88 (1) Ethan, Psalm 89 (1)
Anonymous: (47)
Jewish scholars connected with Kehot Publication also ascribe some of the "anonymous" authorship to Adam, Seth and Abraham.
King David is honored as a Levite, successor of the prophet Samuel and spiritual devotion to the God of the Jewish religion. David not only studied the Scriptures that comprised the Torah but he honored God in psalms daily before daybreak. David's psalms speak of God's attribute, his power, his mercy and his justice, or offer prayers of praise or prayers expressing unlimited trust in God. David is attributed with having collected all the psalms, as some were written before his time by, it is said, Moses, Abraham, Shem and Adam. He added his own compositions to the collection. [See Chabad.org, King David and the Psalms.]
Asaph, or the sons of Asaph [different sources attribute Asaphite psalms in one of these two ways], is usually attributed as the author(s) of the twelve psalms listed above. It is not known, however, whether or not Asaph was only the transcriber of David's additional psalms rather than being the author of the Asaphite psalms. It is most likely that, while Asaph may have transcribed additional Davidic psalms--perhaps some of the anonymous ones--as David's trusted choirmaster, prophet, poet and singer, Asaph composed the 12 psalms in his own right.
Additional confusion over the psalms of Asaph relates to their possible status as part of the collection of Asaphite singers' hymns. Asaphites are identified as a choir of temple singers: they were sons of Asaph who were gifted with song and served as the temple choir. The theory is that any of the sons of Asaph may have composed the 12 psalms. Again, while the 12 psalms may have been in the Asaphite choral hymnal, it is most likely that, given Asaph's status with David, Asaph composed the 12 psalms.

The singers, the sons of Asaph, were also at their stations according to the command of David, Asaph, Heman, and Jeduthun the king's seer (2 Chronicles 35:15, ESV)

Asaph was a Levite, the son of Berechiah, from the line of Gershon. As such he was a "seer," or prophet, and the cousin of Heman (Heman, a Korahite, the son of Joel). From the time of King David, Levites provided, along with other duties, the poets, singers and musicians responsible for hymns dedicated to God. Asaph was a skilled poet and singer upon whom David relied and was appointed chief temple musician and choirmaster.

Then David spoke to the chiefs of the Levites to appoint their relatives the singers, with instruments of music, harps, lyres, loud-sounding cymbals, to raise sounds of joy. So the Levites appointed Heman the son of Joel, and from his relatives, Asaph the son of Berechiah; and from the sons of Merari their relatives, Ethan the son of Kushaiah,... (1 Chronicles 15:16-17, www.bible.ca/archeology)

The Sons of Korah, Levites from the line of Kohath, were appointed by David at the same time indicated in the quote just above (1 Chron 15:16-17) as singers and musicians in the temple. As such, they shared the responsibility for composing hymns to God. This is also true of Ethan the Levite and son of Kushaiah. It is mere speculation, but perhaps Merari is one of the authors of the other 47 anonymous hymns in the Psalms.

To the choirmaster: according to The Gittith. A Psalm of the Sons of Korah. How lovely is your dwelling place,O Lord of hosts!My soul longs, yes, faintsfor the courts of the Lord;my heart and flesh sing for joyto the living God. (Psalm 84:1-2 ESV)

Moses, raised in the Egyptian Pharaoh's palace, was actually a Levite from the line of Kohath and, of course, the leader of exodus of the Israelites from the land of Egypt. Moses was exerted influence on the hymnal style through his psalm recorded in Psalm 90. Solomon was the son of King David and was the one who actually built the temple David had promised God. Solomon wrote Psalms 72 and 127. It was for Solomon's future temple that David initiated the reorganization of the duties of the Levites so that, among other changes, the temple would have singers and musicians. This reorganization was possible because the Ark of the Covenant would have a permanent home in the Holy of Holies chamber in the heart of the future Temple of Solomon.