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There's a property of continuous dimension date filters --
both Date Range and Relative Date ones -- which makes them fast to compute.
For a Range filter one should define only one or two boundary date values
(or compute them as MIN / MAX from the dataset when Only Relevant Values is set).
For a Relative filter there's nothing to compute from the dataset at all -- just set the Ancor Date.
It means that one shall not look (most of the time) at the actual values of a date field to set the filter.
On the opposite, for discrete dimension date filters, one should calculate their values to build a filter.
The flip side of a coin with Date Range filter is that the boundaries could be just any other date --
not necessary the dates derived from the actual date field values. Moreover, using Slider as a control
both lower and upper bound are selected (uniformly) from a Calendar. It's easy and convenient.
The way you would like a Slider to behave is contrary to the "nature" of a Date Range filter.
This "nature" is a matter of some frustrating behaviours, such as the one discussed below:
As a resort, you may want to opt for the two Parameters (both lower and upper date)
and set them both as Date / Allowable Values : Range / Step Size : 1 Week.
Thus you would be using a couple if sliders on a view (no single one, sorry).
Hope this could help.