wordpress does not send notifications

Hi.
The solution: "WordPress is not sending emails"

As shown, the letters actually in most cases are sent successfully, they just cut superantispayware mail.ru and rambler. On Gmail I basically came these letters.
The fact that in the administration cherese standard features you have the real address of the sender and delarey will vary. Real will service your hosting provider.
Slightly helps filling in the MX records for your hosting. But again, most likely mail.ru cut.
I found this output(slightly improved analogue of your work) which works 100% and have made them google mail for a domain, well, using the plugin WP-Mail-SMTP configured to send mail with these Gmail mailboxes.
Then it turns out users do not get scared, emails come from the domain of the site and all newsletters, notifications, etc are working.
Well, or to use a non-shared and full hosting.

on localhost not configured SMTP?

try to create a box wordpress@doamin.name once faced with similar problems

First thing, contact your host. I know from experience that at least 50% of these problems are solved by his tekhpodderzhki.