The book included songs with the acrostic "Natan HaAzati", as well as statements known to be attributed to Sabbateans.
It became famous with R' Yaakov Emden's protesting of the alleged Sabbateanism of R' Jonathan Eybeschutz, and even more so with the publication of maskil David Kohn's book Even HaToim.
In 1954, the book "Taalumat Sefer" by Avraham Yaari was published, which theorized that the author was the judge Binyamin Halevi, a student of the Ari, who lived prior to Shabtai Zevi and Sabbateanism.
[9] In 2008, R' Shlomo Kosovski Shachor published the book "Otzar Hemdat Yamim", which further established this opinion.
Historian Meir Benayahu argued that book's author was apparently R' Israel Yaakov Algazi himself.
The book has been extensively used primarily by Sephardic rabbis, and various kabbalistic customs in it were accepted by all Jewish communities.
Rav Avraham Danzig, in Chayei Adam cites Hemdat Yamim as his source for Tefillah Zakka.