Art- Any tips on identifying painter?

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I have in my possession a beautiful painting of a Native American man. I have had this painting which was given to me as a gift many years ago. I have recently taken the painting to a museum expert and an antique art dealer, both of which place my painting between 1856-1910. The painting is in excellent condition, but the frame is worn. Both the experts and myself are unable to track down the history of who painted this amazing piece of art. Apparently, D.H. Mitchell, is not a famous painter. Does anyone out there have any tips as to how to go about tracking the painter and the history of the painting down? I'm at a loss to the next step and it would be interesting to hear other peoples' ideas, tips, or perspectives on my dilemma.