Intentionally making ourselves remember things that never happened I've been reading an interesting book  which makes mostly founded claims. However, there is no reference to any studies in regards to one of the following claims: according to the author, visualizing something that never happened every day for 3 weeks results in a memory which seems as real as any memory of something that did happen

Let's not focus on the 3 weeks statement. The interesting part is the claim that we can actually create memories which are as good as real. I am well aware that our memory is terrible. I've read around about various ways in which our memories can be changed: phrasing questions in a certain way, basing some false information on real information, priming etc.

But can we really make something that behaves just like a real memory, even if we are well aware that in reality, it's just a scenario that we imagined and repeated in our minds multiple times?
If I understood correctly, you are talking about "false memories" in the context of the following definition in (Johnson, M. K., 2001)


  "A false memory is a mental experience that is mistakenly taken to be
  a veridical representation of an event from one's personal past.
  Memories can be false in relatively minor ways (e.g., believing one
  last saw the keys in the kitchen when they were in the living room)
  and in major ways that have profound implications for oneself and
  others (e.g., mistakenly believing one is the originator of an idea or
  that one was sexually abused as a child)." 


From  Scientific American,
September 1997, Vol. 277 # 3,
pages 70-75

This is a an article from 1997 by Elizabeth Loftus that may shed light on your question.
Yes, the information may be outdated and recent research might have expanded on it. In that case, I might edit my answer soon to reflect those updates after completing further readings relating to the topic

If recent developments interest you, in a study published in the journal Science, Tonegawa et. al [associated with RIKEN-MIT Center for Neural Circuit Genetics] manipulated individual neurons to manipulate encoded memories in the brains of mice. Read here.

Misinformation Effect


  My own research into memory distortion goes back to the early 1970s,
  when I began studies of the "misinformation effect." These studies
  show that when people who witness an event are later exposed to new
  and misleading information about it, their recollections often become
  distorted. In one example, participants viewed a simulated automobile
  accident at an intersection with a stop sign. After the viewing, half
  the participants received a suggestion that the traffic sign was a
  yield sign. When asked later what traffic sign they remembered seeing
  at the intersection, those who had been given the suggestion tended to
  claim that they had seen a yield sign. Those who had not received the
  phony information were much more accurate in their recollection of the
  traffic sign.
  
  My students and I have now conducted more than 200 experiments
  involving over 20,000 individuals that document how exposure to
  misinformation induces memory distortion. In these studies, people
  "recalled" a conspicuous barn in a bucolic scene that contained no
  buildings at all, broken glass and tape recorders that were not in the
  scenes they viewed, a white instead of a blue vehicle in a crime
  scene, and Minnie Mouse when they actually saw Mickey Mouse. Taken
  together, these studies show that misinformation can change an
  individual's recollection in predictable and sometimes very powerful
  ways.


False Childhood Memories


  My research associate, Jacqueline E. Pickrell, and I settled on trying
  to plant a specific memory of being lost in a shopping mall or large
  department store at about the age of five. Here's how we did it. We
  asked our subjects, 24 individuals ranging in age from 18 to 53, to
  try to remember childhood events that had been recounted to us by a
  parent, an older sibling or another close relative. We prepared a
  booklet for each participant containing one-paragraph stories about
  three events that had actually happened to him or her and one that had
  not. We constructed the false event using information about a
  plausible shopping trip provided by a relative, who also verified that
  the participant had not in fact been lost at about the age of five.
  The lost-in-the-mall scenario included the following elements: lost
  for an extended period, crying, aid and comfort by an elderly woman
  and, finally, reunion with the family. 
  
  
  
  After reading each story in the booklet, the participants wrote what
  they remembered about the event. If they did not remember it, they
  were instructed to write, "I do not remember this." In two follow-up
  interviews, we told the participants that we were interested in
  examining how much detail they could remember and how their memories
  compared with those of their relative. The event paragraphs were not
  read to them verbatim, but rather parts were provided as retrieval
  cues. The participants recalled something about 49 of the 72 true
  events (68 percent) immediately after the initial reading of the
  booklet and also in each of the two follow-up interviews. After
  reading the booklet, seven of the 24 participants (29 percent)
  remembered either partially or fully the false event constructed for
  them, and in the two follow-up interviews six participants (25
  percent) continued to claim that they remembered the fictitious event.
  Statistically, there were some differences between the true memories
  and the false ones: participants used more words to describe the true
  memories, and they rated the true memories as being somewhat more
  clear. But if an onlooker were to observe many of our participants
  describe an event, it would be difficult indeed to tell whether the
  account was of a true or a false memory. Of course, being lost,
  however frightening, is not the same as being abused. But the
  lost-in-the-mall study is not about real experiences of being lost; it
  is about planting false memories of being lost. The paradigm shows a
  way of instilling false memories and takes a step toward allowing us
  to understand how this might happen in real-world settings. Moreover,
  the study provides evidence that people can be led to remember their
  past in different ways, and they can even be coaxed into "remembering"
  entire events that never happened.


Imagination Inflation


  What happens when people imagine childhood experiences that did not
  happen to them? Does imagining a childhood event increase confidence
  that it occurred? To explore this, we designed a three-stage
  procedure. We first asked individuals to indicate the likelihood that
  certain events happened to them during their childhood. The list
  contains 40 events, each rated on a scale ranging from "definitely did
  not happen" to "definitely did happen." Two weeks later we asked the
  participants to imagine that they had experienced some of these
  events. Different subjects were asked to imagine different events.
  Sometime later the participants again were asked to respond to the
  original list of 40 childhood events, indicating how likely it was
  that these events actually happened to them. Consider one of the
  imagination exercises. Participants are told to imagine playing inside
  at home after school, hearing a strange noise outside, running toward
  the window, tripping, falling, reaching out and breaking the window
  with their hand. In addition, we asked participants questions such as
  "What did you trip on? How did you feel?" In one study 24 percent of
  the participants who imagined the broken-window scenario later
  reported an increase in confidence that the event had occurred,
  whereas only 12 percent of those who were not asked to imagine the
  incident reported an increase in the likelihood that it had taken
  place. We found this "imagination inflation" effect in each of the
  eight events that participants were asked to imagine. A number of
  possible explanations come to mind. An obvious one is that an act of
  imagination simply makes the event seem more familiar and that
  familiarity is mistakenly related to childhood memories rather than to
  the act of imagination. Such source confusion when a person does not
  remember the source of information can be especially acute for the
  distant experiences of childhood.


Impossible Memories


  A procedure for planting "impossible" memories about experiences that
  occur shortly after birth has been developed by the late Nicholas
  Spanos and his collaborators at Carleton University. Individuals are
  led to believe that they have well-coordinated eye movements and
  visual exploration skills probably because they were born in hospitals
  that hung swinging, colored mobiles over infant cribs. To confirm
  whether they had such an experience, half the participants are
  hypnotized, age-regressed to the day after birth and asked what they
  remembered. The other half of the group participates in a "guided
  mnemonic restructuring" procedure that uses age regression as well as
  active encouragement to re-create the infant experiences by imagining
  them.. Spanos and his co-workers found that the vast majority of their
  subjects were susceptible to these memory-planting procedures. Both
  the hypnotic and guided participants reported infant memories.
  Surprisingly, the guided group did so somewhat more (95 versus 70
  percent). Both groups remembered the colored mobile at a relatively
  high rate (56 percent of the guided group and 46 percent of the
  hypnotic subjects). Many participants who did not remember the mobile
  did recall other things, such as doctors, nurses, bright lights, cribs
  and masks. Also, in both groups, of those who reported memories of
  infancy, 49 percent felt that they were real memories, as opposed to
  16 percent who claimed that they were merely fantasies. These findings
  confirm earlier studies that many individuals can be led to construct
  complex, vivid and detailed false memories via a rather simple
  procedure. Hypnosis clearly is not necessary.




Sources:

The formation of false memories. 
Loftus, E. F. &amp; Pickrell, J. E. (1995). 
Psychiatric Annals, 25, 720-725.

Imagination Inflation: Imagining A Childhood Event Inflates Confidence That It Occurred. 
Maryanne Carry, Charles G. Manning, Elizabeth F. Loftus and Steven J. Sherman  Psychonomic Bulletin and Review, Vol. 3, No. 2, pages 208-214; June 1996.

Remembering Our Past: Studies In Autobiographical Memory. 
Edited by David C. Rubin. 
Cambridge University Press, 1996.



Additional Reading:

Crisis or Creation: A systematic examination of false memory claims.  Dallam, S. (2002). 
Journal of Child Sexual Abuse 9 (3/4): 9–36. 

False Memories Affect Behavior. 
Association for Psychological Science  (2008, August 20).