Does pseudo force induce friction on a body at rest? Suppose I am travelling in a non-inertial (accelerating) frame of reference and I observe a body at rest, will the body be experiencing a kinetic/static/limiting friction with respect to me ?
 A: A book is on the floor of a train which is accelerating relative to the ground.
The frame of reference is attached to the train (and the book).
Yes, there is a static frictional force on the book due to the floor to provide the force necessary to accelerate the book relative to the ground  and the frictional force will be in the direction of the acceleration of the train.
If the train acceleration is even greater then there will come a time when there is a maximum static frictional force on the book due to the floor and the book will be on the point of moving relative to the floor.
Above such an acceleration of the train the book will be observed to accelerate backwards relative to the train with a kinetic frictional force acting on the book due to the train now acting in the same direction as the acceleration of the train.
The pseudo-force acting on the book will still be the same.  
The frictional forces are there irrespective of where the observer is.
In other words both you on the train and your friend on the ground will "observe" the same frictional force.
In the example it is the normal reaction (a real force) which is responsible for the production of the frictional force.
For you, if you want to use Newton's laws whilst on the accelerating train, you have to also include a pseudo-force acting on the book so that when the book is not moving relative to you or the floor the static frictional force is equal and opposite to the pseudo-force.  
Another way of looking at this is to say that the acceleration of free fall as measured on the train is now the vector sum of the acceleration of free fall on the Earth $\vec g$ and the acceleration of the train.
The normal reaction on the book of mass $m$ will still be the same $-m \vec g$ and so the frictional force will still be the same.  
That pseudo force would also have to be included when the book is moving relative to the floor.  
