The 27-year-old actor died from "blunt traumatic asphyxia" in a freak accident at his Los Angeles home last month when his car rolled backward and trapped him against his gate and his parents Irina Korina and Viktor Yelchin conveyed their appreciation for the tributes that have since poured in for the star.
In an ad placed in The Hollywood Reporter, they said: "Thank you, to all of you who have sent flowers and gifts, for your condolences and kind words. We are deeply grateful for your unconditional love. He would be surprised at how many hearts and souls he touched."
Anton was mourned at a private service by close friends and family and buried in an "undisclosed location" five days after his death at his home in Studio City, California.
On the night he died, Anton was due at rehearsals but when he failed to show up, his worried friends went to his home to check on him and found his lifeless body.
An investigation is also being held into whether Anton's car was a model that should have been recalled because of a gear-shifting problem.
