Emergency services were called to a property on Jedworth Road in Glagow on Thursday, April 22 around 5.55pm following a concern call.
Craig Shaw, aged 45, was pronounced dead at the scene and a murder investigation was launched.
Police have been working to piece together Mr Shaw’s last movements, and have said that he was last seen entering the building where he lived around 7.25pm on Wednesday, April 21.
Detective Chief Inspector Cameron Miller, of the Major Investigation Team, said: "Our enquiries have so far established that Mr Shaw was murdered between 7.25pm on Wednesday and 5.55pm on Thursday.
"We believe he may have been deceased for several hours before his body was discovered.
"He sustained a brutal attack and we are determined to trace whoever is responsible and bring them to justice.
"Mr Shaw was well-known locally and I believe there are people in the community who know who is responsible for his murder.
“On Wednesday afternoon, officers carried out a stop and speak operation to prompt the memories of members of the public who may have been in the same area last week.
"This was a worthwhile exercise and I have been encouraged by the response from the public.”
The police have spoken to around 60 people in the area and have thanked the public for their assistance.
He continued: "We are continuing to carry out door-to-door enquiries and review CCTV footage from in and around the area.
"I am appealing to anyone who was in the Jedworth Road area between 7.25pm on Wednesday, 21 April, and 5.55pm on Thursday, 22 April, to come forward.
"In particular, I am urging anyone who visited the building where Mr Shaw lived between these times to contact us if you have not already spoken to officers.
"We are reviewing CCTV footage of those coming and going from the building and would encourage anyone who visited during those times to make themselves known so that they can be eliminated from enquiries.
"Please do not assume that we know the information you may hold.
"Any piece of information you have - no matter how small or insignificant you think it is - could be vital to our investigation and may help us complete the bigger picture.
"I can assure you that any information you provide will be treated with the utmost confidence.
“If you have not yet spoken to police and have information about the murder, please contact us via 101, quoting reference number 2750 of 22 April. Alternatively, Crimestoppers can be contacted anonymously on 0800 555 111.
"We have also set up a website that gives members of the public access to a form to send information directly to the Major Investigation Team.
"You can select to remain anonymous when submitting information. The portal can be accessed here.
"I would like to reassure the local community that we are doing everything we can to identify whoever is responsible.
"A highly visible police presence is in place in the area and that will remain while our investigation continues.
"If you have any concerns or information in connection with our investigation, please speak to our officers who will be carrying out patrols."